Thread: Ratio Test

Can someone help me with the this ratio test. I am having problems canceling things and taking the limit.

Use the ratio test to determine convergence or divergence or that the Ratio Test is inconclusive.

Thanks
AC

Ratio test - Wikipedia, the free encyclopedia

see the formula

a_n is what you have a_(n+1) is what you get by adding 1 i.e. ((n+1)^50)/(n+1)!

noteworthy: (n+1)! = n! * (n+1)

divide it out, play with it a bit, and see if you can get something out of it.

Ok I understand how to to use the ratio test I would get the lim(|(n+1)^50/(n+1)!|*|n!/n^50|) I get it down to lim(|(n+1)^50/((n+1)*n^50)|) but Im not sure how to make it work from here . . .
thanks

Originally Posted by Casas4

Ok I understand how to to use the ratio test I would get the lim(|(n+1)^50/(n+1)!|*|n!/n^50|) I get it down to lim(|(n+1)^50/((n+1)*n^50)|) but Im not sure how to make it work from here . . .
thanks

Use the Binomial expansion on the numerator, then divide each term in the numerator and denominator by the highest power of .

Another way for the limit:







as n goes to infinity

since 0<1 ---> The series converges by the Ratio Test.
PS: There is no need for the absolute values since n>1 here.