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S is the set of all fractions defined by the formula n/(n + 1), where

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Bunuel
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S is the set of all fractions defined by the formula n/(n + 1), where [#permalink] New post  14 Jun 2019, 00:53
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S is the set of all fractions defined by the formula 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. 1/20
B. 1/21
C. 1/2
D. 19/40
E. 19/20

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CareerGeek
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Re: S is the set of all fractions defined by the formula n/(n + 1), where [#permalink] New post  14 Jun 2019, 01:02
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Bunuel wrote:
S is the set of all fractions defined by the formula 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. 1/20
B. 1/21
C. 1/2
D. 19/40
E. 19/20



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
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LeoN88
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Re: S is the set of all fractions defined by the formula n/(n + 1), where [#permalink] New post  14 Jun 2019, 01:22
Bunuel wrote:
S is the set of all fractions defined by the formula 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. 1/20
B. 1/21
C. 1/2
D. 19/40
E. 19/20


t1=1/2
t2=2/3
t3=3/4

t19= 19/20
t1*t2*t3...t19= 1/20 A
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shuvodip04
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Re: S is the set of all fractions defined by the formula n/(n + 1), where [#permalink] New post  14 Jun 2019, 11:25
Bunuel wrote:
S is the set of all fractions defined by the formula 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. 1/20
B. 1/21
C. 1/2
D. 19/40
E. 19/20


Given n is an integer and 0<n<20

So the set will contain the terms when n=1 till n=19
Let t(n) = n/n+1

t(1) = 1/2
t(2) = 2/3
t(3) = 3/4
t(4) = 4/5
.
.
.
.
t(19) = 19/20

Product of all the terms \(=\frac{1}{2} * \frac{2}{3} * \frac{3}{4} * \frac{4}{5} .............\frac{19}{20} = \frac{1}{20}\)

Correct ans : A
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Aprajita760
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Re: S is the set of all fractions defined by the formula n/(n + 1), where [#permalink] New post  14 Jun 2019, 20:10
Dillesh4096 wrote:
Bunuel wrote:
S is the set of all fractions defined by the formula 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. 1/20
B. 1/21
C. 1/2
D. 19/40
E. 19/20



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

Hi,
do we have to solve the whole expression? Isn't there any formula to calculate the product?
Solving the whole expression would take a lot of time. Please tell if there is any shortcut to it.

Thanks!


Pls Hit Kudos if you like the solution
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ScottTargetTestPrep
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Re: S is the set of all fractions defined by the formula n/(n + 1), where [#permalink] New post  05 Feb 2020, 05:47
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Expert Reply
Bunuel wrote:
S is the set of all fractions defined by the formula 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. 1/20
B. 1/21
C. 1/2
D. 19/40
E. 19/20


We need to evaluate the following product:

1/2 x 2/3 x 3/4 x … x 18/19 x 19/20

However, let’s look at the product of the first 3 values:

1/2 x 2/3 x 3/4 = 1/4

We see that only the first numerator and last denominator remain; thus, the product of all the fractions that are in S is 1/20.

Answer: A
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Re: S is the set of all fractions defined by the formula n/(n + 1), where [#permalink] New post  22 Jan 2021, 09:21
Different approach than what I see posted so far:

1/2 * 2/3 * 3/4 *4/5 ... etc 19/20.

numerator = 19!
denominator = 20!

simplifies to 1/20
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Bunuel
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Re: S is the set of all fractions defined by the formula n/(n + 1), where [#permalink] New post  24 May 2023, 11:58
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Expert Reply
Bunuel wrote:
S is the set of all fractions defined by the formula 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. 1/20
B. 1/21
C. 1/2
D. 19/40
E. 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
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Re: S is the set of all fractions defined by the formula n/(n + 1), where [#permalink]
24 May 2023, 11:58
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