Does this converge?

Homework Statement

I believe this problem diverges.

n_infinity ne^-n^2

heres the same equation: http://img100.imageshack.us/img100/6122/untitledig5.png [Broken]

The Attempt at a Solution

upon pluggin in the n's as a sequence of numbers. it looks as it continues on without bound, so it would diverge, correct?

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also, for another problem...

does this converge or diverge: 1 +1/8 + 2/27 + 2/64 + 1/125 + ...

I first want to say that diverges because it continues on to infinity without bound.
however, could i say instead that it converges to 0?

i need an explanation for this one. Thankyou for any here.

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You mean as n goes to infinity
$$ne^{-n^2}$$ goes to infinity?
What happens to $$e^{-n}$$ as n goes to infinity?

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I see now that it's a series. Use the integral test to show it Converges.
CC

1+1/8+2/27+2/64+1/125 +.....can't go to zero because 1+(a bunch of positive things) can't be zero.

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is it safe to say the set of numbers, is divergent since it appears to continue on to infinity without bound?

HallsofIvy
$$\int_0^\infty xe^{-x^2}dx$$
$$\sum_1^\infty \frac{1}{n^3}[/itex] Do you know the "p-series" criterion? For what values of p does [tex]\sum_1^\infty \frac{1}{n^p}[/itex] converge? The integral test would also work nicely for this. Does [tex]\int_1^\infty \frac{1}{x^3} dx$$