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Question Stats:
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24%
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If \(S\) is the set of all fractions defined by the formula \(\frac{n}{n+1}\), where \(n\) is a positive integer less than 20, what is the product of all the fractions that are in \(S\)?
A. \(\frac{1}{20}\)
B. \(\frac{1}{21}\)
C. \(\frac{1}{2}\)
D. \(\frac{19}{40}\)
E. \(\frac{19}{20}\)
A. \(\frac{1}{20}\)
B. \(\frac{1}{21}\)
C. \(\frac{1}{2}\)
D. \(\frac{19}{40}\)
E. \(\frac{19}{20}\)
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If \(S\) is the set of all fractions defined by the formula \(\frac{n}{n+1}\), where \(n\) is a positive integer less than 20, what is the product of all the fractions that are in \(S\)?
A. \(\frac{1}{20}\)
B. \(\frac{1}{21}\)
C. \(\frac{1}{2}\)
D. \(\frac{19}{40}\)
E. \(\frac{19}{20}\)
\(\frac{1}{1+1} * \frac{2}{2+1} * \frac{3}{3+1} * \frac{4}{4+1} * ... * \frac{19}{19 +1} = \)
\(=\frac{1}{2} * \frac{2}{3} * \frac{3}{4} *\frac{4}{5}* ... * \frac{19}{20} = \)
\(=\frac{19!}{20!} = \)
\(=\frac{1}{20}\)
Answer: A
A. \(\frac{1}{20}\)
B. \(\frac{1}{21}\)
C. \(\frac{1}{2}\)
D. \(\frac{19}{40}\)
E. \(\frac{19}{20}\)
\(\frac{1}{1+1} * \frac{2}{2+1} * \frac{3}{3+1} * \frac{4}{4+1} * ... * \frac{19}{19 +1} = \)
\(=\frac{1}{2} * \frac{2}{3} * \frac{3}{4} *\frac{4}{5}* ... * \frac{19}{20} = \)
\(=\frac{19!}{20!} = \)
\(=\frac{1}{20}\)
Answer: A
General Discussion
14 Jun 2019, 01:02
Kudos
Bookmarks
Bunuel
Terms of Set S are 1/2, 2/3, 3/4, . . . . . 18/19, 19/20.
Required Product = 1/2*2/3*3/4* . . . .18/19*19/20
= 1/20
IMO Option A
