mon
Posts:
46
Registered:
12/6/04
|
|
Re: Induction proof
Posted:
Aug 20, 2006 7:40 PM
|
|
>> 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
>
|
|
