What is the sum from n=0 to infinity of 5/(11^n) ?

The sum from n=0 to infinity of 5/(11^n) is 11/2

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sum from n=0 to infinity of 5/(11^n)

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

\frac{11}{2}

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Geometric Test:

\frac{11}{10}

= 5 \cdot \frac{11}{10}

Simplify

5 \cdot \frac{11}{10} : \frac{11}{2}

= \frac{11}{2}

n = 1 \sum \infty (\frac{8 π}{9})^{n}

n = 2 \sum \infty \frac{n !}{6 ^{n}}

k = 1 \sum \infty \frac{6}{k ( k + 2 )}

k = 1 \sum \infty \frac{3}{k}

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

What is the sum from n=0 to infinity of 5/(11^n) ?
The sum from n=0 to infinity of 5/(11^n) is 11/2