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

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

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

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

6

Solution steps

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

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty \frac{1}{6 ^{n}}

Apply Series Geometric Test:

\frac{6}{5}

= 5 \cdot \frac{6}{5}

Simplify

5 \cdot \frac{6}{5} : 6

= 6

n = 2 \sum \infty (\frac{3}{8})^{4 n}

n = 0 \sum \infty \frac{4}{( 1 - 4 n ) ^{2}}

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

n = 2 \sum \infty (\frac{3}{5})^{2 n}

n = 1 \sum \infty \frac{- 1}{8 ^{n}}

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