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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\int \frac{x}{1 - x ^{3}} d x

\frac{d}{d x} (a (2 e^{- 5 x} x - 5 e^{- 5 x} x^{2}))

\int \frac{1}{4 - x} d x

\frac{d}{d x} (\frac{x + 1}{x})

6 x - 3 x

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