suppose that the series cn xn has radius of convergence 7 and the series dn xn has radius of convergence 8. what is the radius of convergence of series (cn + dn)xn ?

Answers

Answer 1

The radius of convergence of the series (cn + dn)xn is less than or equal to 1/10 + 1/11, or approximately 0.206.

The radius of convergence of a power series is a measure of how far from the center the series converges. For a power series ∑cnxn, the radius of convergence is denoted as R and is defined as the reciprocal of the limit superior of the absolute values of the coefficients:

\(R = 1 / lim sup |cn|^{(1/n)\)

Given that the series ∑cnxn has a radius of convergence of 10, we have:

\(lim sup |cn|^{(1/n) }= 1/10\)

Similarly, the series ∑dnxn has a radius of convergence of 11, so:

\(lim sup |dn|^{(1/n)} = 1/11\)

Now, let's consider the series ∑(cn + dn)xn. We want to find its radius of convergence, which we'll denote as R'.

Using the same definition, we have:

\(R' = 1 / lim sup |(cn + dn)|^{(1/n)\)

To simplify this expression, we'll use the triangle inequality:

|(cn + dn)| ≤ |cn| + |dn|

Taking the limit superior of both sides, we have:

lim sup |(cn + dn)| ≤ lim sup (|cn| + |dn|)

Now, let's analyze the right-hand side of the inequality:

lim sup (|cn| + |dn|) = lim sup |cn| + lim sup |dn|

Using the properties of the limit superior, we have:

lim sup |cn| + lim sup |dn| ≤ 1/10 + 1/11

Combining these inequalities, we have:

lim sup |(cn + dn)| ≤ 1/10 + 1/11

Therefore, we can conclude that the radius of convergence of the series ∑(cn + dn)xn is less than or equal to 1/10 + 1/11.

To summarize, the radius of convergence of the series (cn + dn)xn is less than or equal to 1/10 + 1/11.

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The complete question is:

Suppose the series ∑cn xn has a radius of convergence of 10 and the series ∑dn xn has a radius of convergence of 11. What is the radius of convergence of the series ∑(cn + dn)xn?


Related Questions

I will mark BRAINLYLIST if correct plzzzz helppppp

I will mark BRAINLYLIST if correct plzzzz helppppp

Answers

Answer:

107

Step-by-step explanation:

it looks like a right angle

Answer:

The answer is 107 degrees.

Step-by-step explanation:

The sum of all the angle of a triangle must equal 180 degrees. That being said if you grab 180 and subract 44 and 29 from it you get 107 degrees. 107+44+29=180. If this did not equal 180 the answer would be wrong but since it does it is right.

If the volume of a cube-shaped box is 729 cubic inches, which equation would you use to determine
how many 1-inch cubes could fit along one side?
A. s=729−−−√3
B. s=729−−−√
C. s=7292
D. s=7293
HELP ASAP

Answers

Answer:it’s a I was stuck to

Step-by-step explanation:

‼️WILL MARK BRAINLIEST‼️

Answers

A radio is priced at r128.8, including vat.if vat was added at 15%, find the original price of the radio and the of the vat paid

Answers

The original price of the radio is r112, and the VAT paid is r16.8.

What is the original price and VAT paid for a radio priced at R128.8 including VAT?

To find the original price of the radio and the amount of VAT paid, we can use the formula:

Original price = Final price / (1 + VAT rate)

VAT paid = Final price - Original price

Given that the final price of the radio, including VAT, is r128.8 and the VAT rate is 15%, we can substitute these values into the formula:

Original price = 128.8 / (1 + 0.15)

VAT paid = 128.8 - Original price

Calculating the original price:

Original price = 128.8 / 1.15 ≈ r112

Calculating the VAT paid:

VAT paid = 128.8 - 112 ≈ r16.8

Therefore, the original price of the radio is approximately r112, and the VAT paid is approximately r16.8.

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✨PLEASE HELP✨DUE SOON✨

PLEASE HELPDUE SOON

Answers

Answer:

y = -30

Option A

Step-by-step explanation:

y = -2x - 10

y = -5x + 20

We just need to substitute the values of y.

We have to equate both the equation.

-2x -10 = -5x + 20

-2x + 5x = 20 + 10

3x = 30

x = 10

Plug x as 10 in any one of the equation

Let's take the first equation

y = -2x  - 10

y = -2(10) - 10

y = -20 -10

y = -30

coat is 20% off. If the regular price of the coat is $225, what is the sale price of the coat?

Answers

Answer:

$180

Step-by-step explanation:

$225 times .20 = 45 .   225-45=180

Answer:

$180

Step-by-step explanation:

Find 1% of the price.

100% = 225

1% = 225 ÷ 100 = 2.25

100 - 20 = 80% (Percentage of sale price)

80% = 2.25 x 80 = 180

Use the inequality to help you complete the statements.

w > 4

The w in the inequality is the
The 4 in the inequality is the

Answers

The inequality w > 4 can be used to complete the following statements: The w in the inequality is the variable or unknown value being compared with the number 4. It represents an unknown quantity that is greater than 4.

The 4 in the inequality is the constant or known value that the variable w is being compared to. It is a number that is less than w.  

Inequalities use mathematical symbols to compare two values and express their relationship.

In this case, the inequality w > 4 uses the symbol ">" which means "greater than." The inequality indicates that w is larger than 4, so any value of w that is greater than 4 will make the inequality true.

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50 POINTS please help!
quickly

What is the value of sinX?

50 POINTS please help!quicklyWhat is the value of sinX?

Answers

Answer letter B. 5 45 / 41




Obtain the general solution to the equation. +rtan 0 = 6 sec 0 tan 0 de The general solution is r(0)=, ignoring lost solutions, if any.

Answers

The general solution to the equation +rtan 0 = 6 sec 0 tan 0 de is r = 6/cos 0.

This means that r can take any value that satisfies this condition, as long as there are no lost solutions.

To obtain the general solution, we start by simplifying the equation using trigonometric identities. We know that sec 0 = 1/cos 0, and we can substitute this into the equation to get:

r tan 0 = 6/cos 0 tan 0

Dividing both sides by tan 0, we get:

r = 6/cos 0

This is the general solution to the equation, as r can take any value that satisfies this condition. However, it is important to note that there may be lost solutions, which occur when the simplification process involves dividing by a variable that may be equal to zero for certain values of 0. Therefore, it is important to check for such values of 0 that may result in lost solutions.

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I’m a 6th grader I need help on this

Im a 6th grader I need help on this

Answers

Answer:

whats the question? I don't see anything.

70% off
original price!
Abdul wants to buy a cat calendar. The original price is $5.30. What is the sale price?
I need this worked out please

Answers

Answer:

the price with the offer is going to be 1.59$

Step-by-step explanation:

\( \frac{x}{5.30} = \frac{70}{100} \)

\(100(x) = 70(5.30)\)

\(100(x) = 371\)

\( \frac{100(x)}{100} = \frac{371}{100} \)

\(x = 3.71\)

\(70\% \: \: \: of \: \: \: 5.30 \: \: \: is \: \: \: 3.71\)

\(5.30 - 3.71 = 1.59\)

In his science class, Ethan is using a microscope that enlarges objects to 100 times their actual size. If the length of a mosquito is 3.5 millimeters, what is the size as seen under the microscope

Answers

Answer:

350 millimeters

Step-by-step explanation:

3.5 millimeters x 100 = 350 millimeters

Let us factorise the following alg
x4/16-y4/81

Answers

Step-by-step explanation:

this way we get value of x and y

hope it helps ☺️☺️

if u like give thanks

Let us factorise the following algx4/16-y4/81
Let us factorise the following algx4/16-y4/81
Let us factorise the following algx4/16-y4/81
Let us factorise the following algx4/16-y4/81

find the slope from the given table

find the slope from the given table

Answers

(8-7)/(-3-0)= -1/3
the slope is -1/3
I cant really see it it’s so close up

2x+7y=-6
4x-y=18 PLEASE HELP ASAP

Answers

Answer:

Explanation:

2x + 7y = -6
4x - y = 18
———————
-2(2x + 7y = -6)
4x - y = 18
———————-
-4x - 14y = 12
4x - y = 18
———————-
-15y = 30
y = 30/-15 = -2

If y = -2 thus:
2x + 7(-2) = -6
2x - 14 = -6
2x = -6 + 14
2x = 8
x = 8/2 = 4

Therefore, x = 4 and y = -2

9. Maria usually pays $3.10 per pound for her favorite granola. Which of the answers below is
a better deal?
A. 2 pounds for $6.49
B. 3 pounds for $10
C. 5 pounds for $14.75
D. 8 pounds for $28
What’s the answer

Answers

Answer:

c

Step-by-step explanation:

The answer is C. To find the answer all you need to do is divide the money per pound for each option until you find the lowest deal.

A is not a good deal because its about $3.14 for a pound

B is not a good deal because its about $3.33 per pound

D is not a good deal because its $3.50 per pound

C IS a good deal because it's $2.95 per pound

Answer:

c

Step-by-step explanation:

The answer is C. To find the answer all you need to do is divide the money per pound for each option until you find the lowest deal.

A is not a good deal because its about $3.14 for a pound

B is not a good deal because its about $3.33 per pound

D is not a good deal because its $3.50 per pound

C IS a good deal because it's $2.95 per pound

Simplify:
-y + 5 + 7y - 9

Answers

Answer: 6y-4

Step-by-step explanation:

Combine like terms

I WILL GIVE
Create an equivalent expression for this

I WILL GIVE Create an equivalent expression for this

Answers

Answer: C

Step-by-step explanation:

Answer: I think the answer is A.

Step-by-step explanation:

I WILL GIVE Create an equivalent expression for this

how do I solve this?​

how do I solve this?

Answers

ONE THE PROPERTIES OF A RHOMBUS STATES THAT ALL SIDES ARE EQUAL MEANING IF AD IS 39cm THRN BC IS ALSO BC SINCE AD=BC

IF SO THEN IN TRIANGLE BEC WE CAN USE THE THEOREM OF PYTHAGORAS TO FIND EC SINCE WE HAVE THE HYPOTENUSE EQUAL TO 39cm AND THE ADJACENT SIDE EB EQUAL TO 15cm

\( {ec}^{2} = {bc}^{2} - {eb}^{2} \\ {ec}^{2} = ( {39})^{2} - ( {15})^{2} \\ ec = \sqrt{1521 - 225} \\ ec = \sqrt{1296} \\ ec = 36\)

EC=36 cm

HOPE THIS HELPS

what is 37 1/4 x 24 help me

Answers

37 and 1 / 4 = 37 * 6 = 74 * 3 = 222

The production team purchases cans of paint that will cover 60 in2. Write an inequality representing the maximum length of edge b, in inches, when the block is covered with the minimum amount of paint needed for two coats of paint.

Answers

The surface area of an object is the total area covered by the object's surface

The inequality that gives the maximum dimension of a cubic block covered twice with a quantity of paint that will cover 60 in.² is b ≤ √5

Question: The diagram in the question appear missing and an example diagram is included

The given parameters are;

The quantity of paint available = Cans of paint that will cover 60 in.²

The number of coats of paint to apply to the box =  2

Required:

To write an inequality representing the maximum edge length, b, in inches when the block is covered with a minimum amount of paint needed for two coats of paint

Solution:

From the diagram, we have;

The surface area of the cube = 6 × b²

The surface area covered by two coats of paint = 2 × 6 × b²

Therefore, we have;

The area of the block to cover ≤ The quantity of paint available

Which gives

2 × 6 × b² ≤ 60

b² ≤ 60/(2 × 6) = 5

b ≤ √5

The inequality that gives the maximum length of b that can be covered with the minimum amount of paint needed for two coats of paint is b ≤ 5

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The production team purchases cans of paint that will cover 60 in2. Write an inequality representing

Can you devise an argument to show that the sum of any two odd numbers is an even number?

Answers


Let us consider 2 odd numbers, let’s say 2n+1 and 2m+5. As you see for any integral value of n and m, we have the above numbers odd. When we add them,
2n +1 +2m+5 =2(n+m) +6= 2(n+m+3)= EVEN

No matter what is the sum of m and n, Since it got multiplied by 2 it's even and 6 is another even . So the total sum is even.





Please help answer and explain am begging you ​

Please help answer and explain am begging you

Answers

1,6,7 are positive
2,9 are negative
3,4,5,8 are undefined

Answer:

1.) positive

2.) negative

3.) zero

4.) undefined

5.) zero

6.) positive

7.) positive

8.) undefined

9.) negative

Some theories of emotion employ a factor approach. In one conceptualization, the first factor is ________, or how pleasant or unpleasant the stimulus is, and the second factor is ________, or how intense the emotional response is:_________.
a. benignity; excitation
b. excitation; benignity
c. valence; arousal
d. arousal; valence

Answers

Answer:

the answer is c

Pet Designs makes various accessories for pets. Their trademark product, PetBed is perceived to be high quality but not extravagant, and is sold in a variety of pet stores. Wanda Foster, marketing manager, has convinced her boss that they are missing an important segment of the market. "We can increase the quality of the material and design and market PetBed to a higher-end clientele," Wanda claims. We won't compete with our existing product. It's win-win!" PetBeds sell for $50 each. Wanda estimates the gross margin at $35. After working with production engineers and the marketing research team, Wanda has designed a bed that she believes the new market segment will pay $75 for. The production engineers and accountants believe it will cost about $61 to make. If Pet Desig uses cost-plus pricing and prices most products like the original PetBed, what should be the price of the high-end PetBed?

Answers

If Pet Design uses cost-plus pricing and prices most products like the original PetBed, then the price of the high-end PetBed will be $203.33   .

The sales price of the original PetBed is = $50 ;

The Original PetBed gross margin is = $35 ;

So , the ratio of the gross margin is = 35/50 ;

⇒ 0.7 = 70% ,

The cost to make the PetBed that production engineers and accountants believe is = $61 ;

So , The new PetBed cost is = $61 ;

The price of the high end PetBed is = $61/(100% - 70%) ;

= (61)/(30%)

= $203.33 .

Therefore , The price of the high end PetBed is $203.33 .

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The given question is incomplete , the complete question is

Pet Designs makes various accessories for pets. Their trademark product, PetBed is perceived to be high quality but not extravagant, and is sold in a variety of pet stores. Wanda Foster, marketing manager, has convinced her boss that they are missing an important segment of the market. "We can increase the quality of the material and design and market PetBed to a higher-end clientele," Wanda claims. We won't compete with our existing product. It's win-win!"

PetBeds sell for $50 each. Wanda estimates the gross margin at $35. After working with production engineers and the marketing research team, Wanda has designed a bed that she believes the new market segment will pay $75 for. The production engineers and accountants believe it will cost about $61 to make.

If Pet Design uses cost-plus pricing and prices most products like the original PetBed, what should be the price of the high-end PetBed?

Which of the following shows the correct steps in solving the equation?
-8x + 3 = 19

Answers

Answer:

-8x=19-3

-8x=16

x= 16/-8

x=-2

Step-by-step explanation:

Answer:

X=-2 (The steps are shown below.

Step-by-step explanation:

-8x+3=19

-3        -3

-8x=16

-8x/-8=16/-8

x=-2

Joyce paid $39.00 for an item at the store that was 70 percent off the original price. What was the original price?

Joyce paid $39.00 for an item at the store that was 70 percent off the original price. What was the original

Answers

Answer:the answer is 10 because if u subctract it will work

Step-by-step explanation:

A circle has a circumference of
452.16
452.16452, point, 16 units.
What is the radius of the circle?

Answers

The radius of the circle is approximately =71.96 units

What is circle ?

Circles can be defined by their radii and all points on the circumference of a circle are equidistant from the center. Circles are widely used in mathematics, science and engineering for various applications, including modeling and solving problems in geometry.

The formula for the circumference of a circle is 2 * pi * r, where r is the radius.

Given the circumference, we can solve for the radius:

452.16 = 2 * pi * r

r = 452.16 / (2 * pi)

The radius of the circle is approximately 71.96 units.

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What is the answer to 1/4x=2?

Answers

Answer: x=8

Step-by-step explanation: Solve for the x by simplifying both sides of the equation, then isolate the variable.

I hope this help you out!

Solve for x. Round to the nearest tenth.

Solve for x. Round to the nearest tenth.

Answers

The measure of reference angles to problems are,

7. Ф = 41.81°.

8. Ф = 64.23°.

10. Ф = 51.31°.

What are trigonometric ratios in terms of a right-angle triangle?

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

7. With respect to the reference angle opposite and the hypotenuse is given,

sin = opposite/hypotenuse.

sinФ = 4/6.

Ф = sin⁻¹(4/6).

Ф = 41.81°.

8. With respect to the reference angle opposite and adjacent is given,

tan = opposite/adjacent.

tanФ = 29/14.

Ф = tan⁻¹ (29/14).

Ф = 64.23°.

9. With respect to the reference angle opposite and the hypotenuse is given, Similar to problem 7.

10. With respect to the reference angle hypotenuse and adjacent is given,

cos = adjacent/hypotenuse.

cosФ = 25/40.

Ф = cos⁻¹(25/40).

Ф = 51.31°.

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