Question

Which geometric series diverges?

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


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

C.

Answer 1

c

Explanation:

Answer 2

The correct option is C.

Explanation:

A geometric series divergent if
`|r|\geq1`.

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

`a=(2)/(5)`

common ratio is

`r=(3/10)/(3/5) =(1)/(2)`

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,

`a=-10`

common ratio is

`r=(4)/(-10) =-(2)/(5)`

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

`a_n=ar^(n-1)`

So, the common ratio of option C and D are -4 and
`(1)/(5)` respectively.

Since the absolute common ratio in option C is more than 1. i.e.,
`|-4|\geq1`, 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.