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 2020-11-10 Answered
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
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Expert Answer

Margot Mill
Answered 2020-11-11 Author has 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)

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Jeffrey Jordon
Answered 2021-12-16 Author has 2064 answers
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