Question

\[\sum _{k=0}^{\infty } (-1)^{k+1}\left(\frac{1}{3}\right)^k\]

Answer 1

What does it converge to? I know how to do it , want to know other ways

Answer 2

\[=\sum_{0}^{\infty}(-1)*(-1)^{k}*\left(\frac{1}{3}\right)^{k}\]\[=\sum_{0}^{\infty}(-1)*\left(-\frac{1}{3}\right)^{k}\]\[= -\sum_{0}^{\infty}\left(-\frac{1}{3}\right)^{k}\]\[= -\left(\frac{3}{1+3}\right)\]\[= -\frac{3}{4}\]

That's how I'd do it.

Answer 3

imru i posted queston

Answer 4

That's how I did it too

Answer 5

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