What is the sum from n=1 to infinity of n2^n ?

The sum from n=1 to infinity of n2^n is diverges

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sum from n=1 to infinity of n2^n

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

diverges

Solution steps

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

Apply Series Ratio Test:

diverges

= diverges

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

\int \frac{2}{5} - \frac{5}{x} d x

\int \frac{1}{( 11 - 10 x - x ^{2} ) ^{2}} d x

\frac{d}{d x} (\frac{5}{x + 3})

x \to + 0 lim ((1 - 2 x)^{\frac{1}{2}})

What is the sum from n=1 to infinity of n2^n ?
The sum from n=1 to infinity of n2^n is diverges