How do you use the Ratio Test on the series #sum_(n=1)^oo(n!)/(100^n)# ?

1 Answer
May 22, 2018

Answer:

#limnrarroo ((n+1)!)/(100^(n+1))/(n!)/100^n#

Explanation:

#limnrarroo ((n+1)!)/(100^(n+1))/(n!)/100^n#

#limnrarroo ((n+1)!)/(100^(n+1))*(100^n)/(n!)#

#limnrarroo ((n+1))/(100^(n+1))*(100^n)#

#limnrarroo (n+1)/(100)#

#=oo/100=oo#

The Ratio Test states that if this limit is greater than 1, the series diverges. Less than 1, it converges. If it is exactly 1, the test is inconclusive.

Because #oo# is obviously greater than 1, the series diverges.