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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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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? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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