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

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

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

n = 1 \sum \infty \frac{1}{5 ^{n} + 1}

converges

Solution steps

n = 1 \sum \infty \frac{1}{5 ^{n} + 1}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{ln ( n ^{2} )}{n}

n = 1 \sum \infty \frac{5}{n ^{2} + 6}

n = 100 \sum \infty \frac{1}{n}

n = 2 \sum \infty (- 0.4)^{n}

n = 0 \sum \infty π^{- 3 n}

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