Which geometric series diverges?

a. 3/5+3/10+3/20+3/40+

b. -10+4-9/5+16/25-

c.

The correct option is C.

Step-by-step explanation:

A geometric series divergent if .

In the first option the first term of the series is,

common ratio is

Since the common ratio is less than 1, therefore the geometric series is convergent and the option A is incorrect.

In the second option the first term of the series is,

common ratio is

Since the common ratio is less than 1, therefore the geometric series is convergent and the option B is incorrect.

The nth term of a geometric series is in the form of

So, the common ratio of option C and D are -4 and respectively.

Since the absolute common ratio in option C is more than 1. i.e., , therefore the geometric series is divergent and the option C is correct.

Since the common ratio in option D is less than 1, therefore the geometric series is convergent and the option D is incorrect.

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step-by-step explanation: