evaluate each infinite geometric series described a1=3, r=-4

Question

i really need help on this question.

 

Answer 1

The formula for the sum of an INFINITE geometric series  S = a₁/(1 - r ).

Where a₁ is the first term , r is the common ratio.

| r | < 1, the series converges, and the series has a sum.

| r | ≥ 1 , the series diverges and the series does not have sum.

There is no formula for an INFINITE geometric series that diverges.

First term (a₁)  = 3

Common ratio ( r ) = - 4

| r | = | - 4 | = 4 > 1

Since 4 > 1 , the series diverges and the series does not have sum.