What is the sum from k=0 to infinity of (4/7)^k ?

The sum from k=0 to infinity of (4/7)^k is 7/3

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sum from k=0 to infinity of (4/7)^k

k = 0 \sum \infty (\frac{4}{7})^{k}

\frac{7}{3}

Solution steps

k = 0 \sum \infty (\frac{4}{7})^{k}

Apply Series Geometric Test:

\frac{7}{3}

= \frac{7}{3}

x = 1 \sum \infty \frac{x + 2}{x + 1}

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

n = 0 \sum \infty \frac{cos ( πn )}{5}

n = 11 \sum \infty \frac{17}{3 ^{n}}

n = 0 \sum \infty sec (\frac{1}{n ^{2}})

What is the sum from k=0 to infinity of (4/7)^k ?
The sum from k=0 to infinity of (4/7)^k is 7/3