What is the sum from n=0 to infinity of 0.9^{2n} ?

The sum from n=0 to infinity of 0.9^{2n} is 5.26315…

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sum from n=0 to infinity of 0.9^{2n}

n = 0 \sum \infty 0. 9^{2 n}

5.26315 \dots

Solution steps

n = 0 \sum \infty 0. 9^{2 n}

Simplify

0. 9^{2 n} : 0.8 1^{n}

= n = 0 \sum \infty 0.8 1^{n}

Apply Series Geometric Test:

5.26315 \dots

= 5.26315 \dots

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What is the sum from n=0 to infinity of 0.9^{2n} ?
The sum from n=0 to infinity of 0.9^{2n} is 5.26315…