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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 2 \sum \infty n e^{- n^{2}}

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

n = 2 \sum \infty \frac{7}{5 ^{n}}

n = 1 \sum \infty \frac{1}{2 + 3 n}

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

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