Re: [Math4u] Sequence : converges and diverges

If I understand the problem,

Problem 1

We have a series a(1), a(2), a(3), a(4), ...a(n) where

a(1) = 1-1/1

a(2) = 2-1/2

a(3) = 3-1/3

a(n) = n-1/n

It looks to me like the bigger n gets, the closer a(n) gets to n.

So I think we say that as n--> infinity, a(n) approaches n.

problem 2

Here we have a series where the odd terms are zero and the even terms are 2 times the series in problem 1. So this is an interesting situation. The odd terms fall on one line and the even terms approach a slanted line. So you need to look at the precise definition of converging series to see if the series must approach one line or if the series can alternate between 2 lines.

Regards,

Brian Jensen

----- Original Message -----

From: alvi_66

To: Math4u@yahoogroups.com

Sent: Sunday, October 07, 2007 2:55 AM

Subject: [Math4u] Sequence : converges and diverges

I am student of Bs-Mathematics. I need help in this question if
everybody tell me about this question and in future other questions, i
shall be very thankful for this kindness.
Q. Which of the sequence converges, and which diverges? Give reasons
for your answer.
1. an=n-1/n
2. an=((-1)^n+1)(n+1/n)

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