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Topic: Induction proof
Replies: 24   Last Post: Aug 22, 2006 4:11 PM

 Messages: [ Previous | Next ]
 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"

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

Date Subject Author
8/17/06 emailtgs@gmail.com
8/17/06 Lynn Kurtz
8/17/06 Lynn Kurtz
8/17/06 emailtgs@gmail.com
8/17/06 emailtgs@gmail.com
8/17/06 Ben Young
8/17/06 emailtgs@gmail.com
8/18/06 Paul Sperry
8/18/06 emailtgs@gmail.com
8/20/06 Brian M. Scott
8/20/06 emailtgs@gmail.com
8/20/06 Brian M. Scott
8/18/06 Torsten Hennig
8/18/06 emailtgs@gmail.com
8/18/06 Torsten Hennig
8/19/06 emailtgs@gmail.com
8/19/06 mon
8/19/06 Dave L. Renfro
8/20/06 mon
8/20/06 emailtgs@gmail.com
8/20/06 Brian M. Scott
8/19/06 Alexander Bogomolny
8/19/06 Alexander Bogomolny
8/19/06 Dave L. Renfro
8/22/06 Alexander Bogomolny