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S 1, S 2 ,S 3 …......... 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 S 1 2 +S 2 2 +...................S 10 2 is equal to – a> 485,b>495,c>500,d>505

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 S1+S22+...................S10 is  equal to – 
a> 485,b>495,c>500,d>505

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1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
6 years ago
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

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