Math Is Fun Forum

dukebdx12

Member

Registered: 2007-03-21

Posts: 9

Sequences and now Series and Convergence

I just started Calc 3 in summer school and our teacher was not here (monday) the first day of class when we got some notes on ch 9.1 Sequences.....Determining Convergence or Divergence, Squeeze Theoremand determining if it is bounded. (Going by Calculus Eight Edition by Larson,Hostetler, Edwards). Today we moved on to 9.2 which has to deal with Series and Convergence....which i need more help on 9.1 than this.... and a few theorems. I am completely lost right now and have just a slight clue what is going on. The teacher is not all that clear and just puts it on the board and really doesn't explain it. I was wondering if there was a site or someone could explain these 2 sections to me. I have tried reading the book but that hasn't helped much.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Sequences and now Series and Convergence

To get a better understanding of what you're doing we need more information.

Are these sequences and series of real numbers only?  Have you learned the definition of convergence, i.e. for every epsilon greater than 0 there exists an N such that...?  Have you learned Cauchy Criterion?

It would also greatly help if you could post some problems that you are specifically having trouble on.  The one general piece of advice I can give you when it comes to sequences is to forget about intuition and always go back to the definitions.

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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..."

dukebdx12

Member

Registered: 2007-03-21

Posts: 9

Re: Sequences and now Series and Convergence

For example
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.
How do you determine convergence or divergence?

An=( ln sqrt(n) ) / n

An=( n^2/(2n+1)) - (n^2/(2n-1))

Find the sum of the convergent series. ( I got some of these worked but they got tough )

Sum from 1 to inf = 1 / ((2n+1)(2n+3))

sum from 0 to inf = 2 (-2/3)^n

And that is just to name a few.:o