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 = 1 \sum \infty π^{\frac{1}{n}}

n = 0 \sum \infty \frac{4 ^{n}}{n}

n = 0 \sum \infty 4 - \frac{1}{n}

n = 3 \sum \infty \frac{1}{8 e ^{2 n}}

n = 1 \sum \infty (\frac{1}{7})^{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