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What is the value of the following sum? 1/(1*2) + 1/(2*3) +

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What is the value of the following sum? 1/(1*2) + 1/(2*3) +

by Max@Math Revolution » Tue Jun 18, 2019 11:30 pm
What is the value of the following sum?
1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6)

A. 2/3
B. 3/4
C. 4/5
D. 5/6
E. 1
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by GMATGuruNY » Wed Jun 19, 2019 1:41 am
Max@Math Revolution wrote:What is the value of the following sum?
1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6)

A. 2/3
B. 3/4
C. 4/5
D. 5/6
E. 1
x = 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6)
60x = 60[1/2 + 1/6 + 1/12 + 1/20 + 1/30]
60x = 30 + 10 + 5 + 3 + 2
60x = 50
x = 50/60 = 5/6

The correct answer is D.
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by Max@Math Revolution » Fri Jun 21, 2019 12:54 am
=>

Recall that 1/[n*(n+1)] = 1/n - 1/(n+1).

So,
1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6)
= (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6)
= 1/1 - 1/6 = 5/6

Therefore, the answer is D.
Answer: D
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