Hello!

I tried solving the question and the solution comes out to be option (c) 125/64 .

I am explaining the solution below:-

S = 1+ (3/5)+ (6/5^2)+ (10/5^3)+ (15/5^4)+......

=>S/5 = (1/5)+ (3/5^2)+ (6/5^3)+ (10/5^4)+.....

=>4S/5= (1/5)+ (2/5)+ (3/5^2)+ (4/5^3)+ (5/5^3)+....

=>4S/5^2= (1/5)+ (2/5^2)+ (3/5^3)+ (4/5^3)+....

We can take,

(4S/5) - (4S/25)= 1+ (1/5)+ (1/5^2)+ (1/5^3)+.....

=>(16S/25)= 1+ (1/5)+ (1/5^2)+......[Infinite G.P]

We have, a=1 and r=(1/5).

So, S=a/(1-r) =1/(1-1/5) = 1/(4/5)

=>16S/25= 5/4 => S= 125/64.

Hope this cleared your confusion!

Happy learning:)