Series problems--conv. or div?

I have four calculus problems that I haven't been able to figure out. The general question for them is "Test the series for convergence or divergence by explicitly showing the test being used."

I've tried the Limit comparison test, Integral test, Ratio test, and Root test. All failed for me. Here's the questions: (all are series from n=1 to infinity, i didn't know how to use this forum's math type)

1. 10^n/n!

2. sin(n)

3. (2n)^n/n^(2n)

4. n^2/e^((n)^3)

Any and all help is greatly appreciated!