Question

For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5*/4*?

Answer 1

1/5

Explanation:

If k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k inclusive. Inclusive means 1 and k values will be included as the integers.

To get value of 5*;

Since 5 is greater than 1, the fraction in form if 1/t where t is the integer between 1 and 5 inclusive are;

1/1, 1/2, 1/3, 1/4 and 1/5 since 1,2,3,4 and 5 are the values between 1 and 5 "inclusive"

5* will be the product of this fractions i.e 1×1/2×1/3×1/4×1/5 = 1/120

Similarly for 4*;

the fraction in form if 1/t where t is the integer between 1 and 4 inclusive are;

1/1, 1/2,1/3 and 1/4 since 1,2,3 and 4 are the values between 1 and 4 "inclusive"

4* value will be the product of this fractions i.e 1× 1/2×1/3 ×1/4 = 1/24

5*/4* = (1/120)/(1/24)

5*/4* = 1/120×24/1

5*/4* = 1/5