What is the sum from n=0 to infinity of 1/(n3^n) ?

The sum from n=0 to infinity of 1/(n3^n) is converges

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sum from n=0 to infinity of 1/(n3^n)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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

k = 0 \sum \infty (- \frac{3}{10})^{k}

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

n = 1 \sum \infty \frac{9}{n ( n + 9 )}

n = 1 \sum \infty e^{an}

What is the sum from n=0 to infinity of 1/(n3^n) ?
The sum from n=0 to infinity of 1/(n3^n) is converges