What is the sum from n=0 to infinity of (n+1)/(10^n) ?

The sum from n=0 to infinity of (n+1)/(10^n) is converges

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sum from n=0 to infinity of (n+1)/(10^n)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty (0)^{n}

n = 1 \sum \infty - \frac{1}{1 4 ^{n}}

n = 0 \sum \infty \frac{2 n}{2 n + 1}

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

n = 0 \sum \infty \frac{n}{1 - n}

What is the sum from n=0 to infinity of (n+1)/(10^n) ?
The sum from n=0 to infinity of (n+1)/(10^n) is converges