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

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

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sum from n=1 to infinity of 1/(nsqrt(n))

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

converges

Solution steps

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

Simplify

n n : n^{\frac{3}{2}}

= n = 1 \sum \infty \frac{1}{n ^{\frac{3}{2}}}

Apply p-Series Test:

converges

= converges

\int_{\frac{3}{2}}^{\frac{5}{2}} e^{- s t} d t

y^{^{'}} = 4 - y

\int (\frac{2}{x ^{3}} + \frac{3}{x ^{2}} + 5) d x

\frac{e ^{- s}}{s ( s + 2 )}

x \to 0 lim (x^{2} cos (\frac{9}{x}))

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