1. ## 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

2. 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.

3. 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

4. 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 $n$.

5. Another way for the limit:

$\frac{(n+1)^{50}}{(n+1) \, n^{50}}$

$=\left( \frac{n+1}{n} \right)^{50} \cdot \frac{1}{n+1}$

$=\left( 1+\frac{1}{n} \right)^{50} \cdot \frac{1}{n+1}$

$=(1)^{50} \cdot (0)=0$ 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.