S_1,S₂,S₃ …......... are the sum of infinite geometric series whose first terms are 1,2,3.......... and whose common ratios ½,1/3,1/4, respectivel,then S₁² +S₂²+...................S₁₀² is equal to –

a> 485,b>495,c>500,d>505

Using Sn = a/(1-r) for infinite GP

S1=2
S2= 3
S3= 4
.
.
.
S10=11
S₁²+S₂²+...................S₁₀² = 2² + 3² + . . . . 11²
= 1² + 2² + 3² + . . . . 11² – 1²
= sum of square of first 11 natural number – 1
= n(n+1)(2n+1)/6 -1
= 11(12)(23)/6 -1
= 505