Induction Problems for Assignment - Elementary Functions | MATH 112, Assignments of Mathematics

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Math 112

Post chapter 12 Induction Problems (2)

1. Using induction, prove for all positive integers n:

∑^ n

i=

i(i + 1) =

n(n + 1)(n + 2) 3

2. Using induction, prove for all positive integers n:

∑^ n

i=

(2i − 1)^3 = n^2 (2n^2 − 1)

4. Using the induction assumption that n > n + 1, show the next step is true, i.e. ((n + 1) > (n + 1) + 1). Why is the statement n > n + 1 for all positive integers n not true if you just proved that the induction step worked?