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

The sum from n=1 to infinity of (0.5)^n is 1

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

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

1

Solution steps

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

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

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

n = 0 \sum \infty 0. 5^{n} = 2

= 2 - 0. 5^{0}

Simplify

= 1

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