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What is the value of 1/(5*6) + 2/(6*8) + 3/(8*11) + 4/(11*15

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What is the value of 1/(5*6) + 2/(6*8) + 3/(8*11) + 4/(11*15

by Max@Math Revolution » Mon Sep 30, 2019 11:23 pm
[GMAT math practice question]

What is the value of 1/(5*6) + 2/(6*8) + 3/(8*11) + 4/(11*15)?

A. 1/10
B. 3/10
C. 3/14
D. 2/15
E. 3/16
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by Max@Math Revolution » Thu Oct 03, 2019 4:57 am
=>

Remember the following properties.
1/n(n+1) = 1/n - 1/(n+1).
2/n(n+2) = 1/n - 1/(n+2).
3/n(n+3) = 1/n - 1/(n+3).
4/n(n+4) = 1/n - 1/(n+4).
...
Then we have
1/(5*6) + 2/(6*8) + 3/(8*11) + 4/(11*15)
= (1/5-1/6)+(1/6-1/8)+(1/8-1/11)+(1/11-1/15)
= 1/5 - 1/15
= 2/15

Therefore, D is the answer.
Answer: D
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