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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

n = 1 \sum \infty \frac{1}{7 n + 3}

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

n = 0 \sum \infty e^{- 0.2 n}

n = 1 \sum \infty \frac{4}{n - 1}

n = 0 \sum \infty 2 (\frac{1}{5})^{n + 1}

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