Question

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

Answer 1

(1-1/4)(1-1/9)(1-1/16)...(1-1/144) = (1-1/2²)(1-1/3²) .... (1-1/12²) = (2²-1)(3²-1)...(12²-1)/2²3...12² = (2-1)(2+1)(3-1)(3+1)... (11-1)(11+1)(12-1)(12+1)/2²3²...12² = 1*3*2*4*3*5*...*10*12*11*13/2²3²...11²12² = 1*2*3*3*4*4*5*5*...*10*10*11*11*12*13 / 2²3²...11²12² = 2*12*13/2²12² = 13/24