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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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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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*  [#permalink]

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14 Sep 2018, 00:42
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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 $$\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)}$$

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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert 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] ### Show Tags 14 Sep 2018, 01:55 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 _________________ CEO 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] ### Show Tags 14 Sep 2018, 06:54 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 _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor 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] ### Show Tags 16 Sep 2018, 18:34 => $$\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)} = (\frac{1}{1} – \frac{1}{2}) + (\frac{1}{2} – \frac{1}{3}) + (\frac{1}{3} – \frac{1}{4}) + … + (\frac{1}{99} – \frac{1}{100}) = \frac{1}{1} – \frac{1}{100} = 1 – \frac{1}{100} = \frac{99}{100}$$ after cancellation of the inner terms. Therefore, the answer is D. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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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