Problem Set 1.2

#2-Induction Proof Case k=1 – Left side:Right side: Induction step: assume true for k. For k+1, – Left side: – Using – assumption: – This is the desired right side.

#2 - continued Aside – note you used this in Calculus to study when a geometric series converges and, if so, what it converges to. That is, if r<1, then the series converges to:

#3- Induction using 2 nd Principle For k=1, both sides are Assume true for all naturals 1,2,3, … k For case k+1, left side (using hint): Note the use of the assumption for k and k-1

#6 - Induction Check for k=4, left side is 24, right side is 16. Assume true for case k, then for case k+1, left: by our assumption To get to the right, use So