What is the sum from n=0 to infinity of 3/(nsqrt(n)) ?

The sum from n=0 to infinity of 3/(nsqrt(n)) is converges

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sum from n=0 to infinity of 3/(nsqrt(n))

n = 0 \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

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What is the sum from n=0 to infinity of 3/(nsqrt(n)) ?
The sum from n=0 to infinity of 3/(nsqrt(n)) is converges