What is the sum from n=1 to infinity of (0.1)^{n-1} ?

The sum from n=1 to infinity of (0.1)^{n-1} is converges

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sum from n=1 to infinity of (0.1)^{n-1}

n = 1 \sum \infty (0.1)^{n - 1}

converges

Solution steps

n = 1 \sum \infty 0. 1^{n - 1}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=1 to infinity of (0.1)^{n-1} ?
The sum from n=1 to infinity of (0.1)^{n-1} is converges