What is the sum from n=1 to infinity of 3/(nsqrt(n)) ?

The sum from n=1 to infinity of 3/(nsqrt(n)) is converges

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sum from n=1 to infinity of 3/(nsqrt(n))

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

= 3 \cdot n = 1 \sum \infty \frac{1}{n n}

Simplify

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

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

Apply p-Series Test:

converges

= 3 converges

= converges

f (x) = x^{3}, g (x) = 4 x

\frac{d}{d x} ((2 x^{3} + x^{2} - 6 x)^{\frac{2}{3}})

x \to 2 lim (\frac{x}{x ^{2} - x - 2})

\int_{0}^{6} 2 x^{2} - 16 x + 30 d x

\frac{d}{d x} (- 4 e^{- 2 x^{2}} x)

What is the sum from n=1 to infinity of 3/(nsqrt(n)) ?
The sum from n=1 to infinity of 3/(nsqrt(n)) is converges