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

Answer:

The value of p would be $\frac{1}{50}$

Step-by-step explanation:

Given,

$p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right )$

$p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{49} \right )\left ( 1 - \frac{1}{50} \right )$

$p=\frac{2-1}{2}.\frac{3-1}{3}.\frac{4-1}{4}......\frac{49-1}{49}.\frac{50-1}{50}$

$p=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{48}{49}.\frac{49}{50}$

$p=\frac{1.2.3.4.........48.49}{2.3.4........49.50}$

$p=\frac{1}{50}$

Hence, the value of p is 1/50.