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

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

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

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

converges

Solution steps

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

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

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

Apply Series Integral Test:

converges

= \frac{1}{2} converges

= converges

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

k = 3 \sum \infty \frac{1}{( k - 2 ) ^{3}}

n = 0 \sum \infty \frac{i ^{2 n}}{2 n}

k = 1 \sum \infty \frac{1}{k k}

n = 0 \sum \infty 7 + \frac{5}{n ^{5}}

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