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

1 Answer
charredwind
May 22, 2018

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.

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