Date: Aug 20, 2006 7:40 PM
Author: mon
Subject: Re: Induction proof
>> I want to understand why

>> 1/(n+1)^2 < 1/(n*(n+1))

I am talking about the same thing but more informally. I just wrote "I"

instead of "You":)

"Dave L. Renfro" <renfr1dl@cmich.edu> wrote in message

news:1156024536.128486.292580@i42g2000cwa.googlegroups.com...

> 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

>