How do you find the sum of the infinite geometric series given #a_1=14#, r=7/3?
1 Answer
Oct 27, 2016
For a series to have a finite sum the general term of the series must tend to zero when
Explanation:
In other words,
But the general term of the given series is
A couple of remarks:

The condition
#a_n rarr 0# is not sufficient: the series#sum 1/n# is not convergent although#1/n rarr 0# 
In the case of a geometric series (such as the one given) if the absolute value of the ratio
#r > 1# the series diverges.