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

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

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

n = 0 \sum \infty n e^{n^{2}}

diverges

Solution steps

n = 0 \sum \infty n e^{n^{2}}

Apply Series Ratio Test:

diverges

= diverges

r = 1 \sum \infty \frac{3 ^{r}}{r}

n = 1 \sum \infty \frac{6}{5 ^{n}}

n = 0 \sum \infty \frac{2 ^{n}}{n ^{4}}

n = 1 \sum \infty (0.7)^{n}

n = 0 \sum \infty (- \frac{1}{3})^{n - 1}

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