Thread: mathematical induction

Here is the problem:

Prove, by induction, that the sum (-1)^k (2k+1) from k=1 to 2n is proportional to n, and find the constant of proportionality.

Well I don't know how to start the induction part but I have a hunch that the constant of proportionality is just going to be 2.

Thank you

Originally Posted by Percent09

Here is the problem:

Prove, by induction, that the sum (-1)^k (2k+1) from k=1 to 2n is proportional to n, and find the constant of proportionality.

Well I don't know how to start the induction part but I have a hunch that the constant of proportionality is just going to be 2.

Thank you

The base case is trivial (everything is proportional to 1), so let n = 2. Then


So assume that the theorem is true for some n = N. Then we need to show that it is true for n = N + 1. Let the constant of proportionality be 2, since this is true of the n = 2 case.




This is proportional to N + 1 with a constant of proportionality 2. So etc, etc.

-Dan