What is the sum from n=0 to infinity of 5/(8^n) ?

The sum from n=0 to infinity of 5/(8^n) is 40/7

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sum from n=0 to infinity of 5/(8^n)

n = 0 \sum \infty \frac{5}{8 ^{n}}

\frac{40}{7}

Solution steps

n = 0 \sum \infty \frac{5}{8 ^{n}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 5 \cdot n = 0 \sum \infty \frac{1}{8 ^{n}}

Apply Series Geometric Test:

\frac{8}{7}

= 5 \cdot \frac{8}{7}

Simplify

5 \cdot \frac{8}{7} : \frac{40}{7}

= \frac{40}{7}

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

k = 1 \sum \infty (cos (1))^{k}

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

k = 2 \sum \infty (- 0.65)^{k}

n = 2 \sum \infty (\frac{3}{7})^{2 n}

What is the sum from n=0 to infinity of 5/(8^n) ?
The sum from n=0 to infinity of 5/(8^n) is 40/7