Consider the infinite series defined by

∞ ∑ (2n! /2^(2n))

n=1

(a) What is the value of r from the ratio test?

(b) What does this r value tell you about the series?

(a) The ratio r is not a constant ratio, but increases by 1/4 for each term. It begins with 1/2, then it goes up to 3/4, then to 1 and 1.25.......etc.

(b) The value of r tells you that the series will diverge to infinity as r gets larger and larger.