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

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New post 15 Mar 2019, 00:10
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A
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C
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Question Stats:

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

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New post 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

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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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New post 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
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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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New post 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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New post 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

Answer: C
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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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