Prove the following using induction:

1. 1+3+5+7++2n1=n^2.
2. (8|(3^(2n)1) for all n 0.
3. 2^n n! for n 4.
4. Prove for all positive integersn, the quantity( n^5)/5+(n^4)/2+(n^3)/3n/30is an integer.