Question

Which geometric series diverges?

Answer 1

Answer:

The correct option is C.

Step-by-step explanation:

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

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

$a=\frac{2}{5}$

common ratio is

$r=\frac{3/10}{3/5} =\frac{1}{2}$

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

$r=\frac{4}{-10} =-\frac{2}{5}$

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 $\frac{1}{5}$ 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.

Answer 2

C on ingenuity. and i need more words so that is it