Question

(1-1/4). (1-1/9). 1- (1/16).....(1-1/144)

 

Answer 1

`= 3/4 . 8/9 . 15/16. ... . 143/144`

`= (1.2.3...12)/(2.3.4....12) . (3.4.....12.13)/(2.3....11.12)`

`= 1/12 . 13/2 = 13/24`

Answer 2

=(1-1/2)(1+1/2)(1-1/3)(1+1/3)*...*(1-1/12)(1+1/12)

=1/2*2/3*...*11/12*3/2*4/3*...*13/12

=1/12*13/2=13/24