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

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

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

n = 0 \sum \infty 5 (\frac{7}{8})^{n}

40

Solution steps

n = 0 \sum \infty 5 (\frac{7}{8})^{n}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty (\frac{7}{8})^{n}

Apply Series Geometric Test:

8

= 5 \cdot 8

Simplify

= 40

n = 0 \sum \infty \frac{1}{n ^{6} + 1}

n = 0 \sum \infty \frac{3 n}{n !}

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

n = 0 \sum \infty \frac{i}{n ( n + 1 )}

n = 1 \sum \infty \frac{5 ^{n}}{n ^{3}}

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