Question

Please solve fully

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.8 − 11 +

121

8

  −

1331

64

  +  

Step 1

To see 8 − 11 +

121

8

  −

1331

64

  +    as a geometric series, we must express it as

∞	ar n − 1
n = 1

.

For any two successive terms in the geometric series

∞	ar n − 1
n = 1

, the ratio of the the two terms,

ar n

ar n − 1

, simplifies into an algebraic expression given by  

$$r

   .

Step 2

In our series 8 − 11 +

121

8

  −

1331

64

  +   , the ratio

−   1331 64

121 8

is r = -11/8  

-11/8

.

Step 3

In the series 8 − 11 +

121

8

  −

1331

64

  +   , the n = 3 term is

121

8

.

If this is to equal ar ² = a

−

11

8

	2

, then a = 8  

8

.

Step 4

Similarly, −

1331

64

  =  

−

11

8

	3

.

Answer 1