1. Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer.
2. Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer.
3. Use mathematical induction to show that 3 divides n^3+2n whenever n is a nonnegative integer.