Geometric Series: Convergent or Divergent?

Identify each series as being convergent or divergent. If is convergent, compute its sum. If it is divergent, explain how you know.

1.

)

&*(

16 3 9 2

&'(

Diverges: đ?‘&#x; ≼ 1

2.

12 48 192 −3 + − + −⋯ 5 25 125

Convergent, because đ?‘&#x; = − Sum: đ?‘† =

'7 ('

8 ' 9

=

'5 7

4 5

3.

)

;*(

7 1 − 6 4

;'(

Convergent, because đ?‘&#x; = Sum: đ?‘† =

< = >? (' 8

=

(4 (5

'( 4

4.

)

B*(

𝜋 𝑒

B

Divergent:

C 7

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