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InterviewSolution
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If N, the set of natural numbers is partitionaed into groups `S_(1)={1},S_(2)={2,3},S_(3)={4,5,6,7},S_(4)={8,9,10,11,12,13,14,15},"....",` find the sum of the numbers n `C_(50).` |
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Answer» The numbers of terms in the groups are `1,2,2^(2),2^(3),"…."` `therefore` The number of terms in the 50th group `=2^(50-1)=2^(49)` `therefore` The first term of 1st group `=1=2^(0)=2^(1-1)` The first term of 2nd group `=2=2^(1)=2^(2-1)` The first term of 3rd group `=4=2^(2)=2^(3-1)` `vdots" "vdots " " vdots " "vdots " " vdots "` The first term of 50th group `2^(50-1)=2^(49)` ` therefore S_(50)=(2^(49))/(2){2xx2^(49)+(2^(49)-1)xx1}` ` =2^(48)(2^(50)+2^(49)-1)` ` =2^(48)[(2^(49)(2+1)-1]=2^(48)(3*2^(49)-1)` |
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