#### To determine

Whether the geometric series is convergent or divergent and obtain the sum if the series is convergent.

#### Answer

The series is divergent.

#### Explanation

**Given:**

The series is
3−4+163−649+⋯
.

Here,
a=3 and r=−43.

**Result used:**

The geometric series
∑n=1∞arn−1 (or) a+ar+ar2+⋯
is divergent if
|r|≥1
, where *a* is the first term and *r* is the common ratio of the series.

**Calculation:**

The first term of the series is
a=3
.

The common ratio of the series is,

r=Second termFirst term=−43

The absolute value of *r* is,

|r|=|−43|=43=1.33>1

Since
|r|>1
and by using the Result stated above, the series is divergent.

Therefore, the series is divergent.