What is the sum from n=1 to infinity of (pi/4)^n ?

The sum from n=1 to infinity of (pi/4)^n is 4/(4-pi)-1

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sum from n=1 to infinity of (pi/4)^n

n = 1 \sum \infty (\frac{π}{4})^{n}

\frac{4}{4 - π} - 1

Solution steps

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

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

= \frac{4}{4 - π} - (\frac{π}{4})^{0}

Simplify

= \frac{4}{4 - π} - 1

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What is the sum from n=1 to infinity of (pi/4)^n ?
The sum from n=1 to infinity of (pi/4)^n is 4/(4-pi)-1