What is the sum from n=1 to infinity of 0.7^n+0.9^n ?

The sum from n=1 to infinity of 0.7^n+0.9^n is 11.33333…

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sum from n=1 to infinity of 0.7^n+0.9^n

n = 1 \sum \infty 0. 7^{n} + 0. 9^{n}

11.33333 \dots

Solution steps

n = 1 \sum \infty 0. 7^{n} + 0. 9^{n}

Apply the Sum Rule:

\sum a_{n} + b_{n} = \sum a_{n} + \sum b_{n}

= n = 1 \sum \infty 0. 7^{n} + n = 1 \sum \infty 0. 9^{n}

n = 1 \sum \infty 0. 7^{n} = 2.33333 \dots

n = 1 \sum \infty 0. 9^{n} = 9

= 2.33333 \dots + 9

Simplify

= 11.33333 \dots

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What is the sum from n=1 to infinity of 0.7^n+0.9^n ?
The sum from n=1 to infinity of 0.7^n+0.9^n is 11.33333…