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

The sum from n=0 to infinity of (e^n)/(pi^n) is converges

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sum from n=0 to infinity of (e^n)/(pi^n)

n = 0 \sum \infty \frac{e ^{n}}{π ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{e ^{n}}{π ^{n}}

Apply exponent rule:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= n = 0 \sum \infty (\frac{e}{π})^{n}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=0 to infinity of (e^n)/(pi^n) ?
The sum from n=0 to infinity of (e^n)/(pi^n) is converges