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# What is the value of 2(1-1/2) + 3(1-1/3) + … + 100(1 – 1/100)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the value of 2(1-1/2) + 3(1-1/3) + … + 100(1 – 1/100)?  [#permalink]

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15 Mar 2019, 00:10
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Difficulty:

35% (medium)

Question Stats:

64% (01:26) correct 36% (01:15) wrong based on 33 sessions

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[GMAT math practice question]

What is the value of $$2(1-\frac{1}{2}) + 3(1-\frac{1}{3}) + … + 100(1 – \frac{1}{100})$$?

$$A. 3600$$
$$B. 4800$$
$$C. 4950$$
$$D. 5000$$
$$E. 5050$$

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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" e-GMAT Representative Joined: 04 Jan 2015 Posts: 2803 Re: What is the value of 2(1-1/2) + 3(1-1/3) + … + 100(1 – 1/100)? [#permalink] ### Show Tags 15 Mar 2019, 00:42 Solution Given: • A series = 2 (1 – ½) + 3 (1 – 1/3) + … + 100 (1 – 1/100) To find: • The value of the given series Approach and Working: We can write the individual terms as follows: • 2 (1 – ½) = 2 * ½ = 1 • 3 (1 – 1/3) = 3 * 2/3 = 2 • 4 (1 – ¼) = 4 * ¾ = 3 • 100 (1 – 1/100) = 100 * 99/100 = 99 Therefore, the value of the series = 1 + 2 + 3 + … + 99 = 99 * 100 /2 = 99 * 50 = 4950 Hence, the correct answer is option C. Answer: C _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7230 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the value of 2(1-1/2) + 3(1-1/3) + … + 100(1 – 1/100)? [#permalink] ### Show Tags 17 Mar 2019, 18:19 => Note: This sum has $$100 – 2 + 1 = 99$$ terms. $$2(1-\frac{1}{2}) + 3(1-\frac{1}{3}) + … + 100(1 – \frac{1}{100})$$ $$= (2 – 1) + (3 - 1) + … + (100 – 1)$$ $$= 2 + 3 + … + 100 – ( 1 + 1 + … + 1 )$$ $$= ( 2 + 100 )\frac{99}{2} – 99$$ $$= 51*99 – 99 = (51-1)*99 = 50*99 = 4950$$ Therefore, the answer is C. Answer: C _________________ 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 2(1-1/2) + 3(1-1/3) + … + 100(1 – 1/100)?  [#permalink]

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17 Mar 2019, 22:57
1
MathRevolution wrote:
[GMAT math practice question]

What is the value of $$2(1-\frac{1}{2}) + 3(1-\frac{1}{3}) + … + 100(1 – \frac{1}{100})$$?

$$A. 3600$$
$$B. 4800$$
$$C. 4950$$
$$D. 5000$$
$$E. 5050$$

the series $$2(1-\frac{1}{2}) + 3(1-\frac{1}{3}) + … + 100(1 – \frac{1}{100})$$
upon doing the calculation we observe is a cosective number series from 1 to 99
so sum of n no in series
n * (n+1) /2 = 99 * 100/2
IMO C 4950
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Re: What is the value of 2(1-1/2) + 3(1-1/3) + … + 100(1 – 1/100)?  [#permalink]

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19 Mar 2019, 19:16
MathRevolution wrote:
[GMAT math practice question]

What is the value of $$2(1-\frac{1}{2}) + 3(1-\frac{1}{3}) + … + 100(1 – \frac{1}{100})$$?

$$A. 3600$$
$$B. 4800$$
$$C. 4950$$
$$D. 5000$$
$$E. 5050$$

Simplifying we see that we have:

(2 - 1) + (3 - 1) + ... + (100 - 1) = 1 + 2 + …. + 99

So we see that we need to determine the sum of the consecutive integers from 1 to 99, inclusive:

sum = average x number

sum = (1 + 99)/2 x 99

sum = 50 x 99 = 4950

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Re: What is the value of 2(1-1/2) + 3(1-1/3) + … + 100(1 – 1/100)?   [#permalink] 19 Mar 2019, 19:16
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