
Re: Induction proof
Posted:
Aug 19, 2006 5:55 PM


kp wrote (in part):
> I want to understand why > 1/(n+1)^2 < 1/(n*(n+1))
Statements:
1. 0 < 1
2. n < (n+1)
3. n(n+1) < (n+1)(n+1)
4. 1 / [n(n+1)] > 1 / [(n+1)(n+1)]
Reasons:
1. 1 is a positive number.
2. Add n to both sides of #1.
3. Multiply both sides of #2 by the positive number n+1.
4. Apply the function f(x) = 1/x, which is strictly decreasing for x > 0, to both sides of #3. Recall that "f is strictly decresing for x > 0" means "a < b and a,b > 0 ==> f(a) > f(b)" is true.
Dave L. Renfro

