GATE CE 2018 Set 1 — Question 9
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General Aptitude → Quantitative Aptitude → Series
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Question
Consider a sequence of numbers where , for each integer . What is the sum of the first 50 terms?
Correct answer
(C) (1 + (1)/(2)) - ((1)/(51) + (1)/(52))
Solution
The sum of the first 50 terms is .Expanding the sum:
This is a telescoping series where most terms cancel out:
This matches option (C).
This is a telescoping series where most terms cancel out:
- The from the first term cancels with the from the third term.
- The from the second term cancels with the from the fourth term, and so on.
This matches option (C).
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