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28 Nov 2016, 03:59
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (02:26) correct
69%
(02:24)
wrong
based on 134
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of \(A=\frac{1}{1 \times 2 \times 3}+\frac{1}{2 \times 3 \times 4}+...+\frac{1}{48 \times 49 \times 50}\)?
A. \(\frac{306}{1225}\)
B. \(\frac{637}{2550}\)
C. \(\frac{1175}{4704}\)
D. \(\frac{1199}{4800}\)
E. \(\frac{2497}{9996}\)
A. \(\frac{306}{1225}\)
B. \(\frac{637}{2550}\)
C. \(\frac{1175}{4704}\)
D. \(\frac{1199}{4800}\)
E. \(\frac{2497}{9996}\)
Updated on: 15 Jul 2020, 11:35
Originally posted by BrushMyQuant on 28 Nov 2016, 07:48.
Last edited by BrushMyQuant on 15 Jul 2020, 11:35, edited 1 time in total.
Last edited by BrushMyQuant on 15 Jul 2020, 11:35, edited 1 time in total.
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In these kind of questions our strategy will always be to break down each term into difference of two terms, such that alternate terms cancel out. In thsi case we can do it as follows
\(A=\frac{1}{2} * \frac{2}{1 \times 2 \times 3}+\frac{2}{2 \times 3 \times 4}+...+\frac{2}{48 \times 49 \times 50}\)
\(A=\frac{1}{2} * \frac{3-1}{1 \times 2 \times 3}+\frac{4-2}{2 \times 3 \times 4}+...+\frac{50-48}{48 \times 49 \times 50}\)
\(A=\frac{1}{2} * ( \frac{3}{1 \times 2 \times 3} - \frac{1}{1 \times 2 \times 3} + \frac{4}{2 \times 3 \times 4} - \frac{2}{2 \times 3 \times 4}+...+\frac{50}{48 \times 49 \times 50} - \frac{48}{48 \times 49 \times 50} )\)
\(A=\frac{1}{2} * ( \frac{1}{1 \times 2 } - \frac{1}{2 \times 3} + \frac{1}{2 \times 3 } - \frac{1}{3 \times 4}+...+\frac{1}{48 \times 49} - \frac{1}{49 \times 50} )\)
Now alternate terms will cancel out and we will be left with only two terms
\(A=\frac{1}{2} * ( \frac{1}{1 \times 2} - \frac{1}{49 \times 50} )\)
\(A=\frac{1}{2} * ( \frac{1225-1}{49 \times 50} )\)
\(A=\frac{1}{2} * ( \frac{1224}{49 \times 50} )\)
\(A=\frac{306}{1225}\)
So, answer will be A
Hope it helps!
\(A=\frac{1}{2} * \frac{2}{1 \times 2 \times 3}+\frac{2}{2 \times 3 \times 4}+...+\frac{2}{48 \times 49 \times 50}\)
\(A=\frac{1}{2} * \frac{3-1}{1 \times 2 \times 3}+\frac{4-2}{2 \times 3 \times 4}+...+\frac{50-48}{48 \times 49 \times 50}\)
\(A=\frac{1}{2} * ( \frac{3}{1 \times 2 \times 3} - \frac{1}{1 \times 2 \times 3} + \frac{4}{2 \times 3 \times 4} - \frac{2}{2 \times 3 \times 4}+...+\frac{50}{48 \times 49 \times 50} - \frac{48}{48 \times 49 \times 50} )\)
\(A=\frac{1}{2} * ( \frac{1}{1 \times 2 } - \frac{1}{2 \times 3} + \frac{1}{2 \times 3 } - \frac{1}{3 \times 4}+...+\frac{1}{48 \times 49} - \frac{1}{49 \times 50} )\)
Now alternate terms will cancel out and we will be left with only two terms
\(A=\frac{1}{2} * ( \frac{1}{1 \times 2} - \frac{1}{49 \times 50} )\)
\(A=\frac{1}{2} * ( \frac{1225-1}{49 \times 50} )\)
\(A=\frac{1}{2} * ( \frac{1224}{49 \times 50} )\)
\(A=\frac{306}{1225}\)
So, answer will be A
Hope it helps!
General Discussion
28 Nov 2016, 08:32
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I think this is a 700 level question, its not easy to come up with a quick strategy where you can solve such a problem in almost 2.5 minutes
