What is the sum from n=0 to infinity of 0.5^{2n} ?

The sum from n=0 to infinity of 0.5^{2n} is 1.33333…

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sum from n=0 to infinity of 0.5^{2n}

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

1.33333 \dots

Solution steps

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

Simplify

0. 5^{2 n} : 0.2 5^{n}

= n = 0 \sum \infty 0.2 5^{n}

Apply Series Geometric Test:

1.33333 \dots

= 1.33333 \dots

n = 0 \sum \infty arccos (\frac{1}{n})

n = 0 \sum \infty n e^{n^{2}}

r = 1 \sum \infty \frac{3 ^{r}}{r}

n = 1 \sum \infty \frac{6}{5 ^{n}}

n = 0 \sum \infty \frac{2 ^{n}}{n ^{4}}

What is the sum from n=0 to infinity of 0.5^{2n} ?
The sum from n=0 to infinity of 0.5^{2n} is 1.33333…