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# S1,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

manasa gorthy
39 Points
6 years ago
S1= 1/(1-1/2)=2                                                                                                                             S2= 2/(1-1/3)=3   similarly S10=11                                                                                                   S12+S22+...................S102=22+32+..............112=505
Vamsi Krishna Velpuri
31 Points
6 years ago
S1= 1/(1-1/2)=2                                                                                                                             S2= 2/(1-1/3)=3   similarly S10=11                                                                                                   S12+S22+...................S102=22+32+..............112
=(∑ n2) -1 where n=1 to 11