What is the sum from n=0 to infinity of ((0.8)^n)/7 ?

The sum from n=0 to infinity of ((0.8)^n)/7 is 5/7

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sum from n=0 to infinity of ((0.8)^n)/7

n = 0 \sum \infty \frac{( 0.8 ) ^{n}}{7}

\frac{5}{7}

Solution steps

n = 0 \sum \infty \frac{0. 8 ^{n}}{7}

Apply the constant multiplication rule:

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

= \frac{1}{7} \cdot n = 0 \sum \infty 0. 8^{n}

Apply Series Geometric Test:

5

= \frac{1}{7} \cdot 5

Simplify

\frac{1}{7} \cdot 5 : \frac{5}{7}

= \frac{5}{7}

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

n = 1 \sum \infty \frac{2 n}{5 n - 1}

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

n = 0 \sum \infty \frac{1}{3 ^{2 n + 1}}

n = 0 \sum \infty \frac{6 ^{n}}{5 ^{n}}

What is the sum from n=0 to infinity of ((0.8)^n)/7 ?
The sum from n=0 to infinity of ((0.8)^n)/7 is 5/7