What is the sum from n=0 to infinity of (10/11)^n ?

The sum from n=0 to infinity of (10/11)^n is 11

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sum from n=0 to infinity of (10/11)^n

n = 0 \sum \infty (\frac{10}{11})^{n}

11

Solution steps

n = 0 \sum \infty (\frac{10}{11})^{n}

Apply Series Geometric Test:

11

= 11

i = 0 \sum \infty \frac{1}{2 ^{i}}

n = 3 \sum \infty \frac{4}{7 ^{n}}

n = 2 \sum \infty \frac{1}{3 ( 2 ^{n} )}

n = 70 \sum \infty \frac{3}{n ^{2} + 2 n}

k = 1 \sum \infty (- \frac{1}{3})^{k}

What is the sum from n=0 to infinity of (10/11)^n ?
The sum from n=0 to infinity of (10/11)^n is 11