Thread: Sequences Question Please Help

ok i have this problem in the textbook where An= 3^(n+2)/5^n and i am suppose to determine whether it converges or diverges and if it convergies i have to find the limit... any ideals how to do this?

Originally Posted by Krebs

ok i have this problem in the textbook where An= 3^(n+2)/5^n and i am suppose to determine whether it converges or diverges and if it convergies i have to find the limit... any ideals how to do this?

Try re-writing your problem as

. To show it converges show (i) it's decreasing and (ii) bounded below by 0.

Originally Posted by danny arrigo

Try re-writing your problem as

. To show it converges show (i) it's decreasing and (ii) bounded below by 0.

ok so that means that as n approaches infinity An approaches 0 since An is getting smaller and smaller as n gets larger? and thank you for your help

Originally Posted by Krebs

ok so that means that as n approaches infinity An approaches 0 since An is getting smaller and smaller as n gets larger? and thank you for your help

Yes. More formally you want to show (for decreasing)



I think that is obvious.