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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

k = 5 \sum \infty \frac{6}{k ln ^{2} ( k )}

n = 0 \sum \infty \frac{i}{n ^{4}}

n = 0 \sum \infty \frac{n}{11 n ^{6} + 1}

n = 0 \sum \infty (0.25)^{n}

n = 0 \sum \infty \frac{n}{7 ^{n}}

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