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.
Another way for the limit:
$\displaystyle \frac{(n+1)^{50}}{(n+1) \, n^{50}}$
$\displaystyle =\left( \frac{n+1}{n} \right)^{50} \cdot \frac{1}{n+1}$
$\displaystyle =\left( 1+\frac{1}{n} \right)^{50} \cdot \frac{1}{n+1}$
$\displaystyle =(1)^{50} \cdot (0)=0$ 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.