What is the sum from n=1 to infinity of (7+4/n)^{-n} ?

The sum from n=1 to infinity of (7+4/n)^{-n} is converges

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sum from n=1 to infinity of (7+4/n)^{-n}

n = 1 \sum \infty (7 + \frac{4}{n})^{- n}

converges

Solution steps

n = 1 \sum \infty (7 + \frac{4}{n})^{- n}

Apply Series Root Test:

converges

= converges

n = 0 \sum \infty \frac{n}{n + 3}

n = 0 \sum \infty 5 + 2 (- 1)^{n}

n = 0 \sum \infty 14 (\frac{2}{3})^{n}

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

n = 1 \sum \infty \frac{n - 1}{7 n - 1}

What is the sum from n=1 to infinity of (7+4/n)^{-n} ?
The sum from n=1 to infinity of (7+4/n)^{-n} is converges