Representing functions by power series Identify the functions represented by the following power series. sum_{k=1}^inftyfrac{x^{2k}}{k}

Bergen 2020-10-21 Answered
Representing functions by power series Identify the functions represented by the following power series.
k=1x2kk
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d2saint0
Answered 2020-10-22 Author has 89 answers
Given: A power series: k=1x2kk
It is known that the power series of:
ex=n=0xnn!
ln(1x)=n=0xkk
As the power series of ln(1y) is:
ln(1y)=n=0ykk
So when y=x2
k=1x2kk=ln(1x2)
Thus, the function for the power series k=1x2kk=ln(1x2)
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Jeffrey Jordon
Answered 2021-12-16 Author has 2262 answers

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