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

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mon

Posts: 46
Registered: 12/6/04
Re: Induction proof
Posted: Aug 20, 2006 7:40 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

>> 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
>






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