What is the sum from n=1 to infinity of n(0.9)^n ?

The sum from n=1 to infinity of n(0.9)^n is converges

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sum from n=1 to infinity of n(0.9)^n

n = 1 \sum \infty n (0.9)^{n}

converges

Solution steps

n = 1 \sum \infty n \cdot 0. 9^{n}

Apply Series Ratio Test:

converges

= converges

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e^{x} - x^{e}

What is the sum from n=1 to infinity of n(0.9)^n ?
The sum from n=1 to infinity of n(0.9)^n is converges