What is the sum from k=0 to infinity of (0.9)^k ?

The sum from k=0 to infinity of (0.9)^k is 10

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sum from k=0 to infinity of (0.9)^k

k = 0 \sum \infty (0.9)^{k}

10

Solution steps

k = 0 \sum \infty 0. 9^{k}

Apply Series Geometric Test:

10

= 10

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

n = 0 \sum \infty 0.99 9^{n}

n = 1 \sum \infty \frac{n}{1 + n}

n = 1 \sum \infty (- \frac{4}{5})^{n}

x = 0 \sum \infty \frac{1}{x}

What is the sum from k=0 to infinity of (0.9)^k ?
The sum from k=0 to infinity of (0.9)^k is 10