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

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

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

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

diverges

Solution steps

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

Apply Series Ratio Test:

diverges

= diverges

k = 1 \sum \infty \frac{6}{k}

n = 1 \sum \infty \frac{1}{3 n ^{2} + 9}

n = 1 \sum \infty \frac{1}{3 n ^{2} + 4}

n = 1 \sum \infty \frac{7}{n ^{9}}

n = 0 \sum \infty 1. 1^{n}

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