What is the sum from n=1 to infinity of (0.5)^{n-1} ?

The sum from n=1 to infinity of (0.5)^{n-1} is converges

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sum from n=1 to infinity of (0.5)^{n-1}

n = 1 \sum \infty (0.5)^{n - 1}

converges

Solution steps

n = 1 \sum \infty 0. 5^{n - 1}

Apply Series Ratio Test:

converges

= converges

n = 0 \sum \infty 2^{1 - n}

n = 0 \sum \infty 2 + (- 1)^{n}

n = 1 \sum \infty \frac{n}{n + 7}

n = 0 \sum \infty 2 (3)^{n}

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

What is the sum from n=1 to infinity of (0.5)^{n-1} ?
The sum from n=1 to infinity of (0.5)^{n-1} is converges