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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*  [#permalink]

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Difficulty:   15% (low)

Question Stats: 78% (01:20) correct 22% (02:39) wrong based on 50 sessions

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[Math Revolution GMAT math practice question]

If $$\frac{1}{n(n+1)} = \frac{1}{n} – \frac{1}{(n+1)},$$ then what is the value of $$\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)}$$

$$A. \frac{1}{100}$$
$$B. \frac{1}{50}$$
$$C. \frac{49}{50}$$
$$D. \frac{99}{100}$$
$$E. \frac{1}{2}$$

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7688
Re: If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$\frac{1}{n(n+1)} = \frac{1}{n} – \frac{1}{(n+1)},$$ then what is the value of $$\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)}$$

$$A. \frac{1}{100}$$
$$B. \frac{1}{50}$$
$$C. \frac{49}{50}$$
$$D. \frac{99}{100}$$
$$E. \frac{1}{2}$$

If $$\frac{1}{n(n+1)} = \frac{1}{n} – \frac{1}{(n+1)},$$ ....
So 1/(1*2)=1/1-1/2...
1/(2*3)=1/2-1/3..
So sum = 1-1/2+1/2-1/3......-1/99+1/99-1/100=1-1/100=99/100

D
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CEO  V
Joined: 12 Sep 2015
Posts: 3728
Location: Canada
Re: If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*  [#permalink]

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Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$\frac{1}{n(n+1)} = \frac{1}{n} – \frac{1}{(n+1)},$$ then what is the value of $$\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)}$$

$$A. \frac{1}{100}$$
$$B. \frac{1}{50}$$
$$C. \frac{49}{50}$$
$$D. \frac{99}{100}$$
$$E. \frac{1}{2}$$

If 1/n(n+1) = 1/n – 1/(n+1), then...

1/(1*2) = 1/1 - 1/2
1/(2*3) = 1/2 - 1/3
1/(3*4) = 1/3 - 1/4
.
.
.
1/(98*99) = 1/98 - 1/99
1/(99*100) = 1/99 - 1/100

So, 1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1/(99*100) = (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + . . . (1/98 - 1/99) + (1/99 - 1/100)
= 1/1 - 1/100
= 99/100

Cheers,
Brent
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*  [#permalink]

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=>
$$\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)} = (\frac{1}{1} – \frac{1}{2}) + (\frac{1}{2} – \frac{1}{3}) + (\frac{1}{3} – \frac{1}{4}) + … + (\frac{1}{99} – \frac{1}{100}) = \frac{1}{1} – \frac{1}{100} = 1 – \frac{1}{100} = \frac{99}{100}$$ after cancellation of the inner terms.

Therefore, the answer is D.
Answer: D
_________________ Re: If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*   [#permalink] 16 Sep 2018, 18:34
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# If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*

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