Identify the functions represented by the following power series. ∑k=0∞(−1)kxk3k

David Lewis

David Lewis

Answered

2021-12-23

Identify the functions represented by the following power series. k=0(1)kxk3k

Answer & Explanation

limacarp4

limacarp4

Expert

2021-12-24Added 39 answers

Given series
k=0(1)kxk3k
The Power series representation of (1+x)1 is,
1x+x2x3+=k=0(1)kxk
Replace x by x/3 above we get the given series
k=0(1)kxk3k=(1+x3)1=33+x
Hence, the function represented by the power series
33+x
Result:
33+x

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