Carcass wrote:
S is the set of all fractions of the form \(\frac{n}{n+1}\), where n is a positive integer less than 20.
Quantity A |
Quantity B |
The product of all the fractions that are in S |
\(\frac{1}{20}\) |
Let's get a better idea of what Set S looks like.
We're told that n can have any integer value from 1 to 19 inclusive.
When n = 1, the corresponding fraction is \(\frac{1}{1+1}=\frac{1}{2}\)
When n = 2, the corresponding fraction is \(\frac{2}{2+1}=\frac{2}{3}\)
When n = 3, the corresponding fraction is \(\frac{3}{3+1}=\frac{3}{4}\)
.
.
.
.
.
When n = 18, the corresponding fraction is \(\frac{18}{18+1}=\frac{18}{19}\)
When n = 19, the corresponding fraction is \(\frac{19}{19+1}=\frac{19}{20}\)
So, Quantity B \(= (\frac{1}{2})(\frac{2}{3})(\frac{3}{4})(\frac{4}{5})......(\frac{17}{18})(\frac{18}{19})(\frac{19}{20})\)
\(=\frac{(1)(2)(3)(4)(5)....(17)(18)(19)}{(2)(3)(4)(5)....(17)(18)(19)(20)}\)
\(=\frac{1}{20}\)
We get:
QUANTITY A: \(\frac{1}{20}\)
QUANTITY B: \(\frac{1}{20}\)
Answer: C
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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