What is the sum from n=0 to infinity of n^{1/2} ?

The sum from n=0 to infinity of n^{1/2} is diverges

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sum from n=0 to infinity of n^{1/2}

n = 0 \sum \infty n^{\frac{1}{2}}

diverges

Solution steps

n = 0 \sum \infty n^{\frac{1}{2}}

Apply Series Divergence Test:

diverges

= diverges

n = 0 \sum \infty n^{- \frac{3}{2}}

n = 3 \sum \infty \frac{1}{( n - 2 ) ^{4}}

n = 1 \sum \infty \frac{9}{7 ^{n}}

n = 5 \sum \infty \frac{4}{n ^{2} - n}

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

What is the sum from n=0 to infinity of n^{1/2} ?
The sum from n=0 to infinity of n^{1/2} is diverges