Question

Чему равно произведение : (1-1/4)(1-1/9)(1-1/16)...(1-1/225)?

Answer 1

$(1- \frac{1}{2^2})(1- \frac{1}{3^2})(1- \frac{1}{4^2})...(1- \frac{1}{15^2})=\\\\ = \frac{(2-1)(2+1)}{2^2} \frac{(3-1)(3+1)}{3^2} \frac{(4-1)(4+1)}{4^2} ...\frac{(15-1)(15+1)}{15^2} =\\\\ = \frac{1*2*3^2*4^2*5^2*...*14^2*15*16}{2^2*3^2*4^2*5^2*...*15^2} =\\\\= \frac{1*2*15*16}{2^2*15^2} = \frac{16}{30} = \frac{8}{15}$

Ответ: 8/15