1.Prove by induction that 11n6 is divisible by 5 for every positive integer n.

2. Prove by induction that 2^n>2n for every positive integer n>2.

3. Prove by induction that 1+3+5++(2n1)=n^2.

4. Prove by induction that n! n^n.

5. Prove by induction 1+2++n=n(n+1)/2 for n1.