Find the sum of the following series. $\sum_{m=1}^{ \infty }\frac{{(-1)^m}{+3}}{5^m}$
My attempt
$\sum_{m=1}^{ \infty }$ $\frac{(-1)^m}{5^m}$ + 3$\sum_{m=1}^{ \infty }$ $\frac{1}{5^m}$
But, I am stuck here... Can anyone show how to do this
2026-04-30 03:00:10.1777518010
Find the sum of the following series. $\sum_{m=1}^{ \infty }\frac{{(-1)^m}{+3}}{5^m}$
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Since $\left|-\frac15\right|=\frac15<1$,$$\sum_{m=1}^\infty\frac{(-1)^m}{5^m}=\sum_{m=1}^\infty\left(-\frac15\right)^m=\frac{-\frac15}{1+\frac15}=-\frac16.$$Can you take it from here?