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

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

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

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

converges

Solution steps

n = 1 \sum \infty \frac{1}{n \cdot 3 ^{n}}

Apply Series Ratio Test:

converges

= converges

n = 0 \sum \infty 7

n = 0 \sum \infty - 3 + 4 n^{5}

n = 1 \sum \infty 2 (0.2)^{n - 1}

n = 1 \sum \infty \frac{5}{n ( n + 5 )}

n = 1 \sum \infty 5 - \frac{3}{2 ^{n}}

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