What is the sum from n=3 to infinity of 1/(2^n-5) ?

The sum from n=3 to infinity of 1/(2^n-5) is converges

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sum from n=3 to infinity of 1/(2^n-5)

n = 3 \sum \infty \frac{1}{2 ^{n} - 5}

converges

Solution steps

n = 3 \sum \infty \frac{1}{2 ^{n} - 5}

Apply Series Ratio Test:

converges

= converges

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

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}

What is the sum from n=3 to infinity of 1/(2^n-5) ?
The sum from n=3 to infinity of 1/(2^n-5) is converges