If S=(3/5)+(10/52)+(21/53)+(36/54)+(55/55)+ ldots ldots ldots ∞ then 4 S is equal to

Question

If S=(3/5)+(10/52)+(21/53)+(36/54)+(55/55)+ ldots ldots ldots ∞ then 4 S is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

S =(3/5)+(10/52)+(21/53)+(36/54)+(55/55)+ ldots ldots ∞ ( S /5)=(3/52)+(10/53)+(21/54)+(36/55) ldots . . . subtracting (4/5) S=(3/5)+(7/52)+(11/53)+(15/54)+(19/55) (4/52) S=(3/52)+(7/53)+(11/54)+ ldots subtracting (16/25) S =(3/5)+(4/52)+(4/53)+(4/54)+ ldots =(3/5)+((4/52)/1-(1)5)=(3/5)+(1/5) (16/25) s =(4/5) s =(5/4) ⇒ 4 s =5

Q. If S=53​+5210​+5321​+5436​+5555​+………∞ then 4S is equal to

Q. If $S = \frac{3}{5} + \frac{10}{5 ^{2}} + \frac{21}{5 ^{3}} + \frac{36}{5 ^{4}} + \frac{55}{5 ^{5}} + \dots\dots\dots \infty$ then $4 S$ is equal to