InterviewSolution
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InterviewSolution
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Find the sum `(1^2)/(2)+(3^2)/(2^2)+(5^2)/(2^3)+(7^2)/(2^4)+….oo` |
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Answer» Correct Answer - 17 `S=1^(2)/2+3^(2)/2^(2)+5^(2)/2^(3)+7^(2)/2^(4)+….oo` (1) `rArr1/2s=1^(2)/2^(2)+3^(2)/2^(3)+5^(2)/2^(4)+…oo` (2) `rArr1/2S=1^(2)/2^(2)+3^(2)/2^(3)+5^(2)/2^(4)+…oo` (2) Subtracting (2) from (1), `1/2S=1^(2)/2+8/2^(2)+16/2^(3)+24/2^(4)+32/2^(5)+..oo` (3) Let `S_(1)=8/2^(2)+16/2^(3)+24/2^(4)+32/2^(5)+..oo` (4) `rArr1/2S_(1)=8/2^(3)+16/2^(4)+24/2^(5)+...oo` (5) Subtracting (5) from (4), `1/2S_(1)=8/2^(2)+8/2^(3)+8/2^(4)+8/2^(5)+...oo` Subtracting (5) from (4), `1/2S_(1)=8/2^(2)+8/2^(3)+8/2^(4)+8/2^(5)+...oo` `=(8/2^(2))/(1-1/2)` =4 or `S_(1)=8` Hence, from (3), `1/2S=1/2+8` `rArrS=17` |
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