Yes then just plug into your def, but first you need to "guess" what the limit is
Then show you can make the above as small as you wish or less than epsilon
Q: Use the formal definition of convergence to prove that the sequence tends to a limit.
A: The formal definition is:
A sequence converges to a limit if, given , there is a natural number such that .
Just not too sure on where to start with this one. I'm guessing that splitting up the fraction into and then proving that the latter part tends to a limit would be the way to go?
Thanks in advance for your help
Thanks for the reply.
Well my educated guess will be that the limit is , giving me
Now which is obvious.
In the solutions they've got this:
Let , take , then for all :
, so the sequence tends to .
Just wondering how they took in the first place?
Sorry for the confusion, really not getting this whole epsilon limit business.