What is the sum from n=1 to infinity of 1/(13^n-5^n) ?

The sum from n=1 to infinity of 1/(13^n-5^n) is converges

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sum from n=1 to infinity of 1/(13^n-5^n)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

(1, - 5), (- 5, 5)

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What is the sum from n=1 to infinity of 1/(13^n-5^n) ?
The sum from n=1 to infinity of 1/(13^n-5^n) is converges