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Let Sk, K = 1, 2, ...., 100 denote the sum of the infinite geometric series whose first term is 
and the common ratio is 1/k. Then the value of 
is [JEE 2010]
and the common ratio is 1/k. Then the value of is [JEE 2010]Correct answer is '0003'. Can you explain this answer?
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Verified Answer
Let Sk, K = 1, 2, ...., 100 denote the sum of the infinite geometric s...
Infinite Sum of GP S = a/(1−r) = (k−1)/[k!(1−1/k)] = 1/(k−1)!
(100)2/100! + ∑k=(1 to 100)|(k2−3k+1)Sk|
(100)2/100! + ∑k=(1 to 100) [(k-1)^2 k[(1/(k-1)!]
(100)2/100! + ∑k=(2 to 100)|[(k-1)/(k-2)! - k/(k-1)!|
(100)2/100! 2/1! - 1/0 + 2/1! - 3/2! + 3/2! +.....+ 99/98! - 100/99!
= (100)2/100! + 2 - 1 + 2 - dfrac{100 * 100}{99! * 100}
= 3
(100)2/100! + ∑k=(1 to 100)|(k2−3k+1)Sk|
(100)2/100! + ∑k=(1 to 100) [(k-1)^2 k[(1/(k-1)!]
(100)2/100! + ∑k=(2 to 100)|[(k-1)/(k-2)! - k/(k-1)!|
(100)2/100! 2/1! - 1/0 + 2/1! - 3/2! + 3/2! +.....+ 99/98! - 100/99!
= (100)2/100! + 2 - 1 + 2 - dfrac{100 * 100}{99! * 100}
= 3
Most Upvoted Answer
Let Sk, K = 1, 2, ...., 100 denote the sum of the infinite geometric s...
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Let Sk, K = 1, 2, ...., 100 denote the sum of the infinite geometric series whose first term isand the common ratio is 1/k. Then the value ofis [JEE 2010]Correct answer is '0003'. Can you explain this answer?
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