Question

Можете решить?(1 - 1/4)(1 - 1/9)(1 - 1/16)...(1 - 1/225)

Answer 1

  
 $(1-frac{1}{4})(1-frac{1}{9})(1-frac{1}{16})(1-frac{1}{25})...(1-frac{1}{225})\\ frac{2^2-1}{2^2 } * frac{3^2-1}{3^2} * frac{4^2-1}{4^2} * frac{5^2-1}{5^2}*...*frac{15^2-1}{15^2} \\ frac{(2-1)(2+1)}{4}* frac{(3-1)(3+1)}{9}*frac{(4-1)(4+1)}{16}*...*frac{(15-1)(15+1)}{225} \\ frac{(1*2*3*4*5*...*14)*(3*4*5*6*...*16)}{4*9*16*...*225} = frac{8}{15}$