Thread: Limit of infinite sequence.

The sequence is for x>y>0



Now what i have got is


How do i find the limit when n goes to infinity ?


Edit: I suspect it has somthing to do with (I dont know the correct english word) the rule that when:



Then:

But I am unable to construct two such limits.

Originally Posted by hjortur

The sequence is for x>y>0



Now what i have got is


How do i find the limit when n goes to infinity ?


Edit: I suspect it has somthing to do with (I dont know the correct english word) the rule that when:



Then:

But I am unable to construct two such limits.

Do you know that it converges? If you do, then you know , so you can just take the limit of both sides now.



Just solve for and you're done. If you don't know converges, I would first try to prove that it does and then use the above method.

Having tried out the sequence a few times with various and , it seems like the sequence converges to , which is a solution of the above equation.

I was able to find a:


And the solution is a=x or a=y.
The thing is I need to be able to show that it converges to x, and not y. How would I go about doing that?

The limit is x, not y, because x> y. The initial value is x+y> x (because both x and y are positive) and the sequence decreases. The limit is x basically because it gets to x first!

Jus shortly after writing this message I was able to show that the limit is x. Like i said, I knew the limit is x. But I needed to show that analyticaly.