What is the sum from k=1 to infinity of 1/(7^k+7) ?

The sum from k=1 to infinity of 1/(7^k+7) is converges

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sum from k=1 to infinity of 1/(7^k+7)

k = 1 \sum \infty \frac{1}{7 ^{k} + 7}

converges

Solution steps

k = 1 \sum \infty \frac{1}{7 ^{k} + 7}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{4 ^{n}}{n 3 ^{n}}

n = 2 \sum \infty \frac{1}{e ^{3 n}}

n = 0 \sum \infty \frac{1}{3 e ^{n}}

n = 1 \sum \infty \frac{1}{4 n ^{2} + 1}

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

What is the sum from k=1 to infinity of 1/(7^k+7) ?
The sum from k=1 to infinity of 1/(7^k+7) is converges