Problem Solving

Roland2rule 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?

1) 1/20
2) 1/21
3) 1/2
4) 19/40
5) 19/20

oa is a
any expert here to help me on how to set up the formula to solve this question?

Let's find out the values of few fractions.

We are given that 0 < n < 20; where n is a positive integer

Thus, n: {1, 2, 3, ... , 19}

First fraction = 1/(1 + 1) = 1/2;
Second fraction = 2/(2 + 1) = 2/3;
Third fraction = 3/(3 + 1) = 3/4;
.
.
.
Nineteenth fraction = 19/(19 + 1) = 19/20;

Multiplying all the fractions, we get,

1/2 x 2/3 x 3/4 x 4/5 x ... 19/20 = 1/20; all the numbers will cancel except 1 and 20.

The correct answer: A

Hope this helps!

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Roland2rule 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?

1) 1/20
2) 1/21
3) 1/2
4) 19/40
5) 19/20

oa is a
any expert here to help me on how to set up the formula to solve this question?

S = {1/2 , 2/3, 3/4, 4/5, . . . 17/18, 18/19, 19/20}
So, we want to evaluate: (1/2)(2/3)(3/4)(4/5) . . . (17/18)(18/19)(19/20)

OBSERVE: (1/2)(2/3)(3/4)(4/5) . . . (17/18)(18/19)(19/20)
Notice that the denominator of one fraction is EQUAL to the numerator of the next fraction. So, these values "cancel out" (that is, their product = 1)
So, we get: (1)/2)(2/3)(3/4)(4/5) . . . (17/18)(18/19)(19/20) = (1/1)(1/20) = 1/20

Answer: A

Cheers,
Brent

BTGmoderatorRO wrote: ↑

Sat Sep 16, 2017 7:40 pm

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?

1) 1/20
2) 1/21
3) 1/2
4) 19/40
5) 19/20

oa is a
any expert here to help me on how to set up the formula to solve this question?

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