What is the sum from n=1 to infinity of (10/17)^n ?

The sum from n=1 to infinity of (10/17)^n is 10/7

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sum from n=1 to infinity of (10/17)^n

n = 1 \sum \infty (\frac{10}{17})^{n}

\frac{10}{7}

Decimal

1.42857 \dots

Solution steps

n = 1 \sum \infty (\frac{10}{17})^{n}

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

= n = 0 \sum \infty (\frac{10}{17})^{n} - (\frac{10}{17})^{0}

n = 0 \sum \infty (\frac{10}{17})^{n} = \frac{17}{7}

= \frac{17}{7} - (\frac{10}{17})^{0}

Simplify

\frac{17}{7} - (\frac{10}{17})^{0} : \frac{10}{7}

= \frac{10}{7}

What is the sum from n=1 to infinity of (10/17)^n ?
The sum from n=1 to infinity of (10/17)^n is 10/7