Question

find the Value of (1-1/3)(1-1/4)(1-1/5).....(1-1/100) ​

Answer 1

Answer:

1/50

Step-by-step explanation:

1-1/3 = 2/3

1-1/4 = 3/4

1-1/5 = 4/5

.

.

.

1-1/99 = 98/99

1-1/100 = 99/100

on multiplying ,

(2/3) * ( 3/4) * (4/5) * ....... * (98/99) * (99/100)

You see that the denominator of first term cancel ot with numerator of second term . similarly all the numerators will cancel out leaving :

2/100 = 1/50