Question

p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right ) P is the product, indicated above, of all the numbers of the form 1 – \frac{1}{k}, where k is an integer from 2 to 50, inclusive. What is the value of P

Answer 1

The value of p would be
`(1)/(50)`

Explanation:

Given,

`p = \left ( 1 - (1)/(2) \right )\left ( 1 - (1)/(3) \right )\left ( 1 - (1)/(4) \right )...\left ( 1 - (1)/(50) \right )`

`p = \left ( 1 - (1)/(2) \right )\left ( 1 - (1)/(3) \right )\left ( 1 - (1)/(4) \right )...\left ( 1 - (1)/(49) \right )\left ( 1 - (1)/(50) \right )`

`p=(2-1)/(2).(3-1)/(3).(4-1)/(4)......(49-1)/(49).(50-1)/(50)`

`p=(1)/(2).(2)/(3).(3)/(4)......(48)/(49).(49)/(50)`

`p=(1.2.3.4.........48.49)/(2.3.4........49.50)`

`p=(1)/(50)`

Hence, the value of p is 1/50.