What is the sum from n=1 to infinity of 1/(2^n-9) ?

The sum from n=1 to infinity of 1/(2^n-9) is converges

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sum from n=1 to infinity of 1/(2^n-9)

n = 1 \sum \infty \frac{1}{2 ^{n} - 9}

converges

Solution steps

n = 1 \sum \infty \frac{1}{2 ^{n} - 9}

Apply Series Ratio Test:

converges

= converges

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

n = 1 \sum \infty \frac{7}{n ^{2} + 16}

n = 0 \sum \infty \frac{n}{7 n ^{3} + 1}

n = 0 \sum \infty ln (2 - n)

n = 1 \sum \infty (- 3)^{n - 1}

What is the sum from n=1 to infinity of 1/(2^n-9) ?
The sum from n=1 to infinity of 1/(2^n-9) is converges