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What is the value of the following sum?

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MathRevolution
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What is the value of the following sum? [#permalink] New post   19 Jun 2019, 00:36
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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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D
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LevanKhukhunashvili
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Re: What is the value of the following sum? [#permalink] New post   19 Jun 2019, 00:43
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}=\frac{50}{60}=\frac{5}{6}\)

IMO
Ans: D
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CareerGeek
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What is the value of the following sum? [#permalink] New post   Updated on: 07 Sep 2019, 06:50
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MathRevolution 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


1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6)
—> (2 - 1)/(1*2) + (3 - 2)/(2*3) + (4 - 3)/3*4) + (5 - 4)/(4*5) + (6 - 5)/(5*6)
—> 2/(1*2) - 1/(1*2) + 3/(2*3) - 2/(2*3) + 4/(3*4) - 3/(3*4) + 5/(4*5) - 4/(4*5) + 6/(5*6) - 5/(5*6
—> 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6
—> 1 - 1/6
—> 5/6

IMO Option D

Pls Hit kudos if you like the solution

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Originally posted by CareerGeek on 19 Jun 2019, 00:53.
Last edited by CareerGeek on 07 Sep 2019, 06:50, edited 1 time in total.
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Re: What is the value of the following sum? [#permalink] New post   19 Jun 2019, 02:55
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MathRevolution 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


\(x = \frac{1}{1*2} + \frac{1}{2*3} + \frac{1}{3*4} + \frac{1}{4*5} + \frac{1}{5*6}\)

\(60x = 60[\frac{1}{2} + \frac{1}{6} + \frac{1}{12}+ \frac{1}{20} + \frac{1}{30}]\)

\(60x = 30 + 10 + 5 + 3 + 2\)

\(60x = 50\)

\(x = \frac{50}{60} = \frac{5}{6}\)

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D
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MathRevolution
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Re: What is the value of the following sum? [#permalink] New post   21 Jun 2019, 02:28
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=>

Recall that \(\frac{1}{[n*(n+1)]} = \frac{1}{n} – \frac{1}{(n+1)}.\)

So,
\(\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + \frac{1}{(4*5)} + \frac{1}{(5*6)}\)

\(= (\frac{1}{1} – \frac{1}{2}) + (\frac{1}{2} – \frac{1}{3}) + (\frac{1}{3} – \frac{1}{4}) + (\frac{1}{4} – \frac{1}{5}) + (\frac{1}{5} – \frac{1}{6})\)

\(= \frac{1}{1} – \frac{1}{6} = \frac{5}{6}\)

Therefore, the answer is D.
Answer: D
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Re: What is the value of the following sum? [#permalink]
21 Jun 2019, 02:28
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