# Show that this sequence converges to 0

Hello

I need to show that this sequence converges to 0:
http://img238.imageshack.us/img238/139/77726816.gif [Broken]

Here is my work:
http://img238.imageshack.us/img238/2570/eqlatexlimnrightarrowin.gif [Broken]
There is n factors in the numerator and in the denominator. We can pair each factor one with another:
http://img142.imageshack.us/img142/2570/eqlatexlimnrightarrowin.gif [Broken]

As n goes to infinity the first terms of this limit go to 0, and thus the limit is = 0.

Is my proof acceptable? Can someone show me another way to do it?
Thank you

Last edited by a moderator:

## Answers and Replies

mathman
Your proof is faulty since there is no requirement that r be an integer. However you seem to have the general idea in that once n>r, the additional multipliers as n gets bigger are <1 and approach 0.

Your proof is faulty since there is no requirement that r be an integer. However you seem to have the general idea in that once n>r, the additional multipliers as n gets bigger are <1 and approach 0.

can you suggest me another way to do it?

mathman