Math Is Fun Forum

sumpm1

Member

Registered: 2007-03-05

Posts: 42

Real Analysis Help

Last edited by sumpm1 (2009-04-20 14:59:43)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Real Analysis Help

1. What is the difference between the nth and the mth term in that sequence?

2. Come up with an estimation for:

Using the triangle inequality.  Now generalize.

(Hint: add 0 in a clever way)

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

ksmathwizz

Guest

Re: Real Analysis Help

question for Ricky.

Just wondering why it's important to come up with an estimation for
|x_{n+2} - x_n| ?   I taught that it should start with |x_n - x_m| and expand from there. But its
been a while since I worked with sequences, so i might be completely off. 

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Real Analysis Help

I taught that it should start with |x_n - x_m| and expand from there

This is what he needs to do, yes.  But it is easiest to see how to do this by first figuring out the special case where n = m+2, and then generalizing.  This is why I wrote, "Now generalize."

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."