ind the value of S for an infinite geometric series with r=-2 and a=8

Question

doin a plus on pc and need sum help!

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 )  = 8.

Common ratio ( r ) = - 2.

| r | = | - 2 | = 2 > 1.

Since 2 > 1 , the series diverges and the series does not have sum.