What is the sum from n=1 to infinity of (2^n)/(n3^n) ?

The sum from n=1 to infinity of (2^n)/(n3^n) is converges

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sum from n=1 to infinity of (2^n)/(n3^n)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=1 to infinity of (2^n)/(n3^n) ?
The sum from n=1 to infinity of (2^n)/(n3^n) is converges