Which convergence test to use I need to prove that the following converges: 
$$\sum\limits_{n=0}^{\infty} n^3e^{-n^4}$$
I'm not sure which test to use. I've tried ratio test but it gets messy. I don't think I have any sums to use in the comparison test and the integral test obviously wouldn't work. Thanks

The form of the term seems to ask for the Integral Test since
$$
\int_x^\infty t^3e^{-t^4}\,\mathrm{d}t=\tfrac14e^{-x^4}
$$
