I need to prove this(not sure how to): $\displaystyle \sum_{n=0}^{\infty}{{(-1)^n}{x^n}}$ = $\displaystyle \frac{1}{1+x}$
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Hello, Originally Posted by kezman I need to prove this(not sure how to): $\displaystyle \sum_{n=0}^{\infty}{{(-1)^n}{x^n}}$ = $\displaystyle \frac{1}{1+x}$ $\displaystyle \sum_{n=0}^\infty (-1)^nx^n=\sum_{n=0}^\infty (-x)^n$ Assuming that $\displaystyle |x|<1$ and noting that this is a geometric series, what can you conclude ?
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