Question

Can someone please help?

For the given statement Pn, write the statements P1, Pk, and Pk+1.

2 + 4 + 8 +...+2n=2^(n+1) - 2

Answer 1

The subject is mathematical induction. Read up about it at:
http://en.wikipedia.org/wiki/Mathematical_induction
or other youtube videos.

P1 is the above statement with n=1, i.e.
2+4+....2n = 2^(n+1)-2 ....(1)
P1 would be
2(1)=2^(1+1)-2 ...(2)

Pn is the given statement itself, i.e. statement (1).

Pn+1 is the statement from (1), replacing all appearances of n by (n+1), simplify if possible.

so Pn+1 is
2+4+....+2n+2(n+1) = 2^((n+1)+1)-2 ...(3)

Mathematical induction states that if we can verify that (1) is true, and ASSUMING (2) is true, if we can show that (3) is also true, then (2) is true for all positive integers.

Answer 2

Thanks. I kind of understand this now.

I have everything down to pk+1. There, I am trying to show that the left side equals the right side, correct?

How do I simplify the right side so that it equals the left?

Answer 3

You usually start from the left (3), if possible.
Put n+1 instead of n on the left and rearrange it so it looks like the right-hand side of (3), then you're done.
Can you do that?

Answer 4

Well, I get 2(n+1)=2^(n+1) - 2. I'm not sure how I can get them to match up. Am I missing something?