1922 Find the interval of convergence of the power series, andfind a familiar function

Chapter 9, Problem 19

(choose chapter or problem)

Find the interval of convergence of the power series, and find a familiar function that is represented by the power series on that interval.

$1-x+x^{2}-x^{3}+\cdots+(-1)^{k} x^{k}+\cdots$

Equation Transcription:

$1-x+{{x}^{2}}_{\ }-{x}^{3}+\ \cdot{}\ \cdot{}\ \cdot{}\ +(-1{)}^{k}{x}^{k}+\ \cdot{}\ \cdot{}\ \cdot{}$

Text Transcription:

1 − x + x2− x3+ · · · +(−1)^kx^k+· · ·

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