What is the sum from k=1 to infinity of 1/(11^k) ?

The sum from k=1 to infinity of 1/(11^k) is 1/10

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sum from k=1 to infinity of 1/(11^k)

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

\frac{1}{10}

Decimal

0.1

Solution steps

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

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= k = 0 \sum \infty \frac{1}{1 1 ^{k}} - \frac{1}{1 1 ^{0}}

k = 0 \sum \infty \frac{1}{1 1 ^{k}} = \frac{11}{10}

= \frac{11}{10} - \frac{1}{1 1 ^{0}}

Simplify

\frac{11}{10} - \frac{1}{1 1 ^{0}} : \frac{1}{10}

= \frac{1}{10}

What is the sum from k=1 to infinity of 1/(11^k) ?
The sum from k=1 to infinity of 1/(11^k) is 1/10