Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
Whether the geometric series is convergent or divergent and obtain the sum if the series is convergent.
The series is divergent.
The series is
The geometric series
∑n=1∞arn−1 (or) a+ar+ar2+⋯
is divergent if
, where a is the first term and r is the common ratio of the series.
Consider the given series
Here, the first term of the series is a = 3 and the common ratio of the series is,
r=Second termFirst term=−923=−92⋅13=−32
The absolute value of r is,
and by using the Result stated above, the series is divergent.
Therefore, the series is divergent.