GATE CS 2015 Set 1 — Question 41
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General Aptitude → Quantitative Aptitude → Series
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Question
Correct answer
0.99 to 0.99
Solution
The given summation is .We can use partial fraction decomposition for the term :
Multiply by : Set :
Set : So, .Now, substitute this back into the summation:
This is a telescoping series:
For :
For :
For :
...
For : When we sum these terms, the intermediate terms cancel out:
The sum simplifies to the first term of the first parenthesis and the last term of the last parenthesis:
The final answer is
Multiply by : Set :
Set : So, .Now, substitute this back into the summation:
This is a telescoping series:
For :
For :
For :
...
For : When we sum these terms, the intermediate terms cancel out:
The sum simplifies to the first term of the first parenthesis and the last term of the last parenthesis:
The final answer is
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