Let g (t) = 1/1+4t2, and let be the Taylor series of g about 0. Then: a2n = for n = 0, 1, 2, . . . A2n+1 = for n = 0, 1, 2, . . . The radius of convergence for the series is R = Hint: g is the sum of a geometric series.

Answers

Answer 1

The Taylor series of g about 0 is given by 1 - 4t^2 + 16t^4 - 64t^6 + ... The coefficients a2n and a2n+1 are given by a2n = (-1)^n * 4^n/(2n+1) and a2n+1 = 0. The radius of convergence for the series is R = 1/2sqrt(2).

The Taylor series of g about 0 is given by:

g(t) = ∑[n=0 to infinity] ((-1)^n * 4^n * t^(2n))/(2n+1)

That this is the sum of a geometric series with first term a=1 and common ratio r=-4t^2. Therefore, we can use the formula for the sum of an infinite geometric series to get the Taylor series of g. The formula is:

S = a/(1-r)

Plugging in our values, we get:

g(t) = 1/(1+4t^2) = 1 - 4t^2 + 16t^4 - 64t^6 + ...

To find the coefficients a2n and a2n+1, we just need to look at the terms that have even and odd powers of t:

a2n = (-1)^n * 4^n/(2n+1)

a2n+1 = 0

The radius of convergence for the series is R = 1/2sqrt(2). We can see this by using the ratio test:

lim[n→∞] |a_n+1/a_n| = 4t^2/(2n+3) → 1 as n → ∞

Therefore, the series converges for |t| < 1/2sqrt(2).

To know more about geometric series, visit;

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help pls ;;-;; ye thxs

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Answer:

You still need help? :P

Step-by-step explanation:

Why do economists use market values when calculating GDP?

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Answer:

Economists use market values when calculating GDP, because if they used quantity terms, they would have multiple units of measurement. Whereas, when they use market values, they have one unit of measurement for all products and services.

Step-by-step explanation:

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Answer:

y=-1/2

Step-by-step explanation:

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We would just have to plug the numbers where the variables are.
- (5) + 8(-5)
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- 45 is your answer
-a + 8 b
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An air conditioning repair company has a flat
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Answer:

Step-by-step explanation:

A jewelry box has a volume of 14 cubic inches. The area is 7 square inches. What is the height of the jewelry box.

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Answer:

2 inches

Step-by-step explanation:

a=Lw

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A salesperson at a jewelry store earns ​8% commission each week. Last​ week, Ali sold $450 worth of jewelry. How much did Ali make in​ commission? How much did the jewelry store make from her ​sales?

Answers

Answer:

she earned 36$ and the store earned 409.5

Step-by-step explana

8% of 450

91% of 450

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Answer:

3 coefficient po

Step-by-step explanation:

sana maka tulong

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Answers

Answer:

3x - 2(x +1) =-2

3x - 2x - 2 =-2

x = - 2 +2

x = 0

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Dn80 pipe 88millimeters is According to the plan All openings must be 40mm larger than the pipe. You know that

Answers

Answer:

128mm

Step-by-step explanation:

Given

[tex]Pipe = 88mm[/tex]

[tex]Ope\ nnings = 40mm\ larger[/tex]

Required

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To do this, we simply add 40mm to the length of the pipe.

This gives:

[tex]Ope\ nings = 88mm + 40mm[/tex]

[tex]Ope\ nings = 128mm[/tex]

Hence, the opening must be 128mm

HELP I NEED HELP ASAP

Answers

Answer:

C) Linear

Step-by-step explanation:

To find this, I turned the situation into an expression. The expression representing this would be: 2x + 5 (a linear function). The 2x represents how much his dad gives Joseph weekly. The 5 represents how much Joseph already has.

Hope it helps!

Christina wants to buy shirts that cost $17.00 each. If x represents the number of shirts Christina buys, which equation shows the amount of money (M) she will pay for the shirts?

Answers

Answer: 17x

Step-by-step explanation:

From the question, we are informed that Christina wants to buy shirts that cost $17.00 each and we are further told that x represents the number of shirts Christina buys.

The equation shows the amount of money (M) she will pay for the shirts will be gotten by multiplying the amount of the each shirt by the total number of shirts bought. This will be:

= 17 × x

M = 17x

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Answers

Answer:

It just equals to 2

Step-by-step explanation:

Think of it as 2^1!

1.

The value of anything that has an exponent of 0 is always 1

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Answers

Answer:

11/16 of a second

Step-by-step explanation:

What is the slope of the line that passes through the points (3, -20) and (11, 16)?
please I'm being timed

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Answer:

9/2

Step-by-step explanation:

(3, -20) & (11, 16)

To find the slope of the line that passes through these points, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(16 - (-20)) / (11 - 3)

Simplify the parentheses.

= (36) / (8)

Simplify the fraction.

36/8

= 9/2

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Hope this helps!

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The power of is what it’s called

Solve for x. Round to the nearest tenth as needed

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Step-by-step explanation:

by Pythagoras :

H²= B²+ P²

(7+x)²= x²+ 9²

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plz mark my answer as brainlist plzzzz.

hope this will be helpful to you .

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x= 67°

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Is it possible to construct a triangle with sides of lengths 40, 8, and 30?

Answers

Answer:

No, the two shorter sides must exceed the longer side.

Step-by-step explanation:

Linda is making a mosaic stepping stone to place in
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Answers

Answer:

D 565.2 in

Step-by-step explanation:

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Answers

Answer:

42

Step-by-step explanation:

Chad has a rope that is 24 meters long

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Determine whether the second polynomial is a factor of the first.
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Answer:

No, because the polynomial 6x² + 5x + 54 evaluated at 4 is equal to 170.

Step-by-step explanation:

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A. $2.00
B. $3.00
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Answers

It has to at least be 9.00 bc i got 8.79

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1. $.50 is what percent of $2.00
2. $.02 is what percent of $2.00
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Answers

Answer:

1.

[tex]25\%[/tex]

2.

[tex].04\%[/tex]

3.

[tex]100\%[/tex]

Answer:

1 is 25% because .50 going into 2 00 4 times or 35%

2 is 10% because 02. is 10% of 2.00

4 is 100% because its all of the 2.00

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Answer:

Your answer is

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Mark my answer as brainlist . I need that urgently . Folow me for more answer.

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Answer:

2.06

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Answer:

6:0

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sorrryy I don't know how to delete this so...

Step-by-step explanation:

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step 3. y = 1

step 4. x = -6.

step 5. the answer is (-6, 1).

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Answer:

$25

Step-by-step explanation:

$ 25 the correct answer

0.75 divided by 38.652

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Answer:

0.019404

Step-by-step explanation:

0.75/38.652 is 0.019404.

Answer:

Divide  0.75  by  38.652  =

0.01940391

and

Divide  38.652  by  0.75 =

51.536

Step-by-step explanation:

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