Series to functions Find the function represented by the following series, and find the interval of convergence of the series. (Not all these series are power series.) sum_{k=1}^inftyfrac{x^{2k}}{4^k}

remolatg

remolatg

Answered question

2020-11-10

Series to functions Find the function represented by the following series, and find the interval of convergence of the series. (Not all these series are power series.)
k=1x2k4k

Answer & Explanation

Margot Mill

Margot Mill

Skilled2020-11-11Added 106 answers

We know that k=0xk=11x
Given function is k=0x2k4k
It can be written as k=0x2k4k=k=0(x24)k
Comparing this with equation, we may write
k=0(x24)k=11x24
=44x2 Now, for the function to be convergent,
|x24|<1
|x2|<4
So the solution is -2
Therefore, the given series can be represented as 44x2 and the interval of convergence is (2,2)

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-16Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-27Added 2605 answers

Answer is given below (on video)

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