Thread: limit of a sequence

[img]http://img708.imageshack.us/img708/4042/analysis999.jpg[/img]
I stuck halfway through, any help would be appreciated.
-----------------------------------
Let ε>0 be given.
|x_n - (9/2)| = ......
simplified to:
39/[(4n^3) + 10]
Im stuck here, what do i do next?

Originally Posted by rlkmg

[img]http://img708.imageshack.us/img708/4042/analysis999.jpg[/img]
I stuck halfway through, any help would be appreciated.
-----------------------------------
Let ε>0 be given.
|x_n - (9/2)| = ......
simplified to:
39/[(4n^3) + 10]
Im stuck here, what do i do next?

Well you need to find in terms of

Note that



Now set this equal to epsilon to find big



Now you can start the formal proof e.g

Let and and let then for ...

Originally Posted by TheEmptySet

Thanks so much, this is the part that I dont understand, could you explain how you got from the left to the right of the above equation? I've seen your technique in many examples but i still dont understand how you did the above step. especially getting rid of the 10

Thanks for your help, appreciated

Originally Posted by rlkmg

Thanks so much, this is the part that I dont understand, could you explain how you got from the left to the right of the above equation? I've seen your technique in many examples but i still dont understand how you did the above step. especially getting rid of the 10

Thanks for your help, appreciated

okay I think you are over thinking this lets look at a few numerical examples.

The idea is if you make the denominator of a fraction smaller (divide by a smaller number) the fraction gets bigger for example



So the idea is to make the fraction easier to work with by replacing it with a bigger but simpler fraction.

Thanks, i tried a few examples and i've got more of a hang of it