Which geometric series diverges?A. 3/5+3/10+3/20+3/40+B. -10+4-9/5+16/25-C.

Answer:The correct option is C.Step-by-step explanation:A geometric series divergent if [tex]|r|\geq1[/tex].In the first option the first term of the series is,[tex]a=\frac{2}{5}[/tex]common ratio is[tex]r=\frac{3/10}{3/5} =\frac{1}{2}[/tex]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,[tex]a=-10[/tex]common ratio is[tex]r=\frac{4}{-10} =-\frac{2}{5}[/tex]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 [tex]a_n=ar^{n-1}[/tex]So, the common ratio of option C and D are -4 and [tex]\frac{1}{5}[/tex] respectively.Since the absolute common ratio in option C is more than 1. i.e., [tex]|-4|\geq1[/tex], 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.