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

The sum from n=1 to infinity of (n+1)/(5^n) is converges

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

n = 1 \sum \infty \frac{n + 1}{5 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{n + 1}{5 ^{n}}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{4}{7 ^{n}}

n = 0 \sum \infty (- \frac{9}{10})^{n}

n = 1 \sum \infty \frac{3}{2 ^{n - 1}}

n = 1 \sum \infty \frac{3}{2 ^{2 n - 1}}

n = 0 \sum \infty 5 (- \frac{2}{3})^{n}

What is the sum from n=1 to infinity of (n+1)/(5^n) ?
The sum from n=1 to infinity of (n+1)/(5^n) is converges