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

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

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

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

converges

Solution steps

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

Multiply by the conjugate of

2^{n} - 1 : \frac{4 ^{n} - 1}{2 ^{n} + 1}

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

Simplify

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

Apply Series Ratio Test:

converges

= converges

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