Question

What is the second step to prove that Sn=>2+2^2+2^3+...+2^n=2(2^n-1)?

Show that Sn is valid for n = k + 2.
Assume that Sn is valid for n = k and prove that Sn is valid for n = k + 1.
Show that Sn is valid for n = k.
Verify that Sn is valid for n = 1.

Answer 1

Assume that Sn is valid for n = k and prove that Sn is valid for n = k + 1.

Explanation:

This is the second step in the principal of mathematical induction. The three steps in the principals of mathematical induction are:

1. show that something works for the first case (base or anchor step)

2. assume that it works for any particular step (inductive hypothesis), and then

3. show that it works for the next case (inductive step)

p. 621 in textbook

It's weird that they put steps 2 & 3 together, but it was correct on the test so ¯\_(ツ)_/¯