Problem 11.2

Use mathematical induction to prove that 1 + 2 + 22 + + 2n = 2n+1 1 for all integers n 0.

Problem 11.3

Use mathematical induction to show that 12 + 22 + + n2 =n(n + 1)(2n + 1)6 for all integers n 1.

Problem 11.4

Use mathematical induction to show that 13 + 23 + + n3 =n(n + 1)22 for all integers n 1.

Problem 11.5

Use mathematical induction to show that 11 2+12 3+ +1n(n + 1) =nn + 1 for all integers n 1.