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

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

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

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

n = 1 \sum \infty (\frac{3 π}{4})^{n}

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

n = 1 \sum \infty \frac{10}{n ^{2} + 9}

n = 0 \sum \infty (- \frac{3}{8})^{n}

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

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