What is the sum from k=0 to infinity of (5/6)^k ?

The sum from k=0 to infinity of (5/6)^k is 6

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sum from k=0 to infinity of (5/6)^k

k = 0 \sum \infty (\frac{5}{6})^{k}

6

Solution steps

k = 0 \sum \infty (\frac{5}{6})^{k}

Apply Series Geometric Test:

6

= 6

n = 1 \sum \infty \frac{1 + n}{n ^{2}}

n = 6 \sum \infty \frac{1}{( n - 3 ) ^{4}}

n = 1 \sum \infty \frac{1}{n ^{7} + 8}

n = 0 \sum \infty \frac{3}{- 3 ^{n}}

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

What is the sum from k=0 to infinity of (5/6)^k ?
The sum from k=0 to infinity of (5/6)^k is 6