Math Forum

Re: Induction proof

Dave:

Here's my mail to you:

[START QUOTE]
Dave, hello:

It was not that difficult. But you were not recruiting for Google,

>> I want to understand why
>> 1/(n+1)^2 < 1/(n*(n+1))

I am talking about the same thing but

On 20 Aug 2006 10:29:37 -0700, wrote in

in

On 20 Aug 2006 10:28:12 -0700, wrote in

in

okay, my question is, just how do you decide to go from here ... to
here.

< (1 - 1/n) + 1/(n+1)^2 (by induction hypotheses)
< (1

Yes, all that stuff is great BUT, you missed the point of my question.
WHY is it that you can all the sudden decide to make that

On 18 Aug 2006 08:18:48 -0700, wrote in

in

X-No-Archive:

Alexander Bogomolny wrote:

[snip stuff]

I sent you an e-mail last Fall sometime but didn't
hear back from you.

Ah, my bad. The question was about finite sums. No reason to apply the limits.

Sorry.

A. Bogomolny

It is also possible to bound the series on the leftt with the telescoping series right away:

1/n*n < 1/n * 1/(n-1) = 1/n -