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What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2?  [#permalink]

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29 Mar 2019, 00:19
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[GMAT math practice question]

What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2?

$$A. \frac{49}{50}$$
$$B. \frac{51}{50}$$
$$C. \frac{99}{100}$$
$$D. \frac{101}{100}$$
$$E. \frac{49}{100}$$

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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: 7567 What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2? [#permalink] Show Tags 29 Mar 2019, 06:22 1 MathRevolution wrote: [GMAT math practice question] What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2? $$A. \frac{49}{50}$$ $$B. \frac{51}{50}$$ $$C. \frac{99}{100}$$ $$D. \frac{101}{100}$$ $$E. \frac{49}{100}$$ $$\frac{1}{3C2}+\frac{1}{4C2}+\frac{1}{5C2}+.......\frac{1}{100C2}$$.. $$\frac{2}{3*2}+\frac{2}{4*3}+\frac{2}{5*4}+.......\frac{2}{100*99}$$.. $$2(\frac{1}{3*2}+\frac{1}{4*3}+\frac{1}{5*4}+.......\frac{1}{100*99})$$.. $$2((\frac{1}{2}-\frac{1}{3})+(\frac{1}{3}-\frac{1}{4})+(\frac{1}{4}-\frac{1}{5})+.......(\frac{1}{98}-\frac{1}{99})+(\frac{1}{99}-\frac{1}{100}))$$.. $$2(\frac{1}{2}-\frac{1}{100})=2*\frac{49}{100}$$.. $$\frac{49}{50}$$.. A _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7230 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2? [#permalink] Show Tags 31 Mar 2019, 18:33 => nCr = $$\frac{{ n(n-1)…(n-r+1) }}{{ 1*2*… *r }}$$ So, nC2 = $$\frac{n(n-1)}{2}$$ and 1/nC2 = $$\frac{2}{{n(n-1)}}$$. Recall that $$\frac{1}{{k(k+1)}} = \frac{1}{k} – \frac{1}{(k+1)}.$$ So, 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2 $$= \frac{2}{(2*3)} + \frac{2}{(3*4)} + \frac{2}{(4*5)} + … + \frac{2}{(99*100)}$$ $$= 2{ \frac{1}{(2*3)} + \frac{1}{(3*4)} + \frac{1}{(4*5)} + … + \frac{1}{(99*100)} }$$ $$= 2{ ( \frac{1}{2} – \frac{1}{3} ) + ( \frac{1}{3} – \frac{1}{4} ) + ( \frac{1}{4} – \frac{1}{5} ) + … + ( \frac{1}{99} – \frac{1}{100} ) }$$ $$= 2( \frac{1}{2} – \frac{1}{100} )$$ $$= 2 ( \frac{50}{100} – \frac{1}{100} )$$ $$= 2(\frac{49}{100})$$ $$= \frac{49}{50}$$ Therefore, the answer is A. Answer: A _________________ 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: What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2?   [#permalink] 31 Mar 2019, 18:33
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What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2?

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