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As we can see, the pattern is... \(A=\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+...+\frac{1}{(n) \times (n+1)}\) = \(\frac{n}{n+1}\)
Re: What is the value of 1/(1*2)+1/(2*3)+...+1/(99*100)?
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05 Dec 2016, 18:10
Although I can follow the explanations made in this thread I would not be able to come up with them on my own. How can we make sure that we identify the right pattern in such a question?
Re: What is the value of 1/(1*2)+1/(2*3)+...+1/(99*100)?
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05 Dec 2016, 18:14
VS93 wrote:
Although I can follow the explanations made in this thread I would not be able to come up with them on my own. How can we make sure that we identify the right pattern in such a question?
In general when I see a question with summation of products (numerator or denominator) I try to see if I can express the general term as a difference. This would help us cancel the terms in a summation series...
Re: What is the value of 1/(1*2)+1/(2*3)+...+1/(99*100)?
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01 Jan 2017, 09:09
nguyendinhtuong wrote:
What is the value of \(A=\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+...+\frac{1}{99 \times 100}\)
A. \(\frac{98}{99}\)
B. \(\frac{99}{100}\)
C. \(\frac{100}{101}\)
D. \(\frac{98}{101}\)
E. \(\frac{99}{101}\)
No need to use pen /pencil Ex : 1/(1*2) + 1/(2*3)=2/3 Similarly if u expand it you will find 3/4,4/5 going through. Hence ans last digit 99/100
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Re: What is the value of 1/(1*2)+1/(2*3)+...+1/(99*100)?
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26 Jul 2017, 02:00
nguyendinhtuong wrote:
What is the value of \(A=\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+...+\frac{1}{99 \times 100}\)
A. \(\frac{98}{99}\)
B. \(\frac{99}{100}\)
C. \(\frac{100}{101}\)
D. \(\frac{98}{101}\)
E. \(\frac{99}{101}\)
Best way to solve these kind of questions is to simplify them to a known form. 1/2 + 1/(2x3) + 1/(3x4) + .............+ 1/(99x100)
since 1/(2x3)= 1/6 = 1/2-1/3, In a similar way all terms can be written in to this form =1/2 + 1/2 -1/3 + 1/3 - 1/4 + 1/4- 1/5+............-1/99+1/99-1/100 =1/2 + 1/2 -1/100 (all others cancelled) =1-1/100 = 99/100 B
gmatclubot
Re: What is the value of 1/(1*2)+1/(2*3)+...+1/(99*100)?
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26 Jul 2017, 02:00