GATE EE 2016 Set 1 — Question 37
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General Aptitude → Quantitative Aptitude → Series
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Question
Let where . The value of in the range , such that is _______.
Correct answer
0.28 to 0.31
Solution
The given series is . We know the standard geometric series sum for :
Differentiating both sides with respect to :
Multiplying both sides by :
Since the term is , we have:
Given :
Since , we can divide by :
(taking the positive root as )
The value of is approximately , which falls within the specified range of .
Differentiating both sides with respect to :
Multiplying both sides by :
Since the term is , we have:
Given :
Since , we can divide by :
(taking the positive root as )
The value of is approximately , which falls within the specified range of .
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