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What is 12+16+112+120+130+142+156?

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What is 12+16+112+120+130+142+156?

by Max@Math Revolution » Thu Jun 25, 2020 12:42 am

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[GMAT math practice question]

What is 1/2+1/6+1/12+1/20+1/30+1/42+1/56?

A. 5/7
B. 5/8
C. 7/8
D. 15/56
E. 23/56
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Re: What is 12+16+112+120+130+142+156?

by Max@Math Revolution » Sun Jun 28, 2020 7:12 am
=>
Remember that 1/n(n+1)=1/n-1/n+1.
1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
= 1-1/8 (because the last term of each bracket cancels out the first term of the next bracket, leaving us only the very first and very last terms)
= 7/8

Therefore, C is the correct answer.
Answer: C
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