So I have a homework assignment that has brought me great strain over the past 2 days. No video or online example have been able to help me with this issue either and I don't know where to turn.
After writing the first 6 terms of the series: 0, 1, 3, 7, 15, 31, 63 I come up with an alternate formula of
I then have to prove these formulas are the same using Induction in 3 parts:
- Proving the base case
- Stating my Inductive Hypothesis
- Showing the Inductive Step
I have done Inductive proofs before but I don’t know how to show cases or do manipulations on a recursive formula. I don’t know how to represent when n = k then n = k + 1 or showing the approach by using n = k – 1 then n = k.