What is the sum from n=1 to infinity of (-2/5)^n ?

The sum from n=1 to infinity of (-2/5)^n is -2/7

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sum from n=1 to infinity of (-2/5)^n

n = 1 \sum \infty (- \frac{2}{5})^{n}

- \frac{2}{7}

Solution steps

n = 1 \sum \infty (- \frac{2}{5})^{n}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= n = 0 \sum \infty (- \frac{2}{5})^{n} - (- \frac{2}{5})^{0}

n = 0 \sum \infty (- \frac{2}{5})^{n} = \frac{5}{7}

= \frac{5}{7} - (- \frac{2}{5})^{0}

Simplify

\frac{5}{7} - (- \frac{2}{5})^{0} : - \frac{2}{7}

= - \frac{2}{7}

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What is the sum from n=1 to infinity of (-2/5)^n ?
The sum from n=1 to infinity of (-2/5)^n is -2/7