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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
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
S is the set of all fractions defined by the formula n/(n + 1), where ...

Product of Fractions in Set S

To find the product of all fractions in set S, we need to first list out all the fractions that satisfy the given formula n/(n + 1), where n is a positive integer less than 20.

List of Fractions in Set S
1. 1/2
2. 2/3
3. 3/4
4. ...
5. 18/19
19. 19/20

Calculating the Product
To find the product of all fractions in set S, we simply multiply all the fractions together:
(1/2) * (2/3) * (3/4) * ... * (18/19) * (19/20)

Simplifying the Product
Notice that each numerator cancels out with the denominator of the next fraction, except for 1 in the denominator of the first fraction and 20 in the numerator of the last fraction:
(1/20)

Therefore, the product of all the fractions in set S is 1/20, which corresponds to option A.
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