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

The sum from n=2 to infinity of 1/(sqrt(n*(n+1))) is diverges

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

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

diverges

Solution steps

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

Apply Series Limit Comparison Test:

diverges

= diverges

f (x) = x^{2} (x^{2} - 8)

(1 + y^{2}) (d x) = x d y

\frac{\partial}{\partial y} (e^{3 x} cos (8 y))

\int e^{- t} d t

\int_{0}^{1} \frac{1}{1 - x} d x

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