What is the sum from n=0 to infinity of (n+1)/(3^n) ?

The sum from n=0 to infinity of (n+1)/(3^n) is converges

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sum from n=0 to infinity of (n+1)/(3^n)

n = 0 \sum \infty \frac{n + 1}{3 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n + 1}{3 ^{n}}

Apply Series Ratio Test:

converges

= converges

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

n = 0 \sum \infty (- \frac{1}{7})^{n}

n = 1 \sum \infty \frac{1}{n ^{8}}

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

n = 0 \sum \infty (- 1)^{2 n}

What is the sum from n=0 to infinity of (n+1)/(3^n) ?
The sum from n=0 to infinity of (n+1)/(3^n) is converges