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 Integral Test:

converges

= converges

f (x) = \frac{1}{8 x}

\frac{d}{d x} ((x + 1)^{- 1})

\int (2 x + 2 y) d y

\frac{d}{d x} (ln (\frac{7 x + 8}{4 x + 8}))

y = \frac{( 3 x ^{2} - x - 2 )}{3 x ^{2}}

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