Question

Вычислите: (1-1/4)*(1-1/9)*(1-1/16)**(1-1/225) подскажите как решать,

Answer 1

$(1-\frac{1}{4})*(1-\frac{1}{9})*...*(1-\frac{1}{225})=$
$\frac{(4-1)*(9-1)*(16-1)*...*(225-1)}{4*9*16*225}=$
$\frac{(2^2-1^2)*(3^2-1^2)*(4^2-1^2)*...*(15^2-1^2)}{2^2*3^2*4^2*...*15^2}=$
$\frac{(2-1)*(2+1)*(3-1)*(3+1)*(4-1)*(4+1)*...*(15-1)*(15+1)}{2^2*3^2*4^2*...*15^2}=$
$\frac{1*3*2*4*3*5*4*6*...12*14*13*15*14*16}{2^2*3^2*4^2*...*14^2*15^2}=$
$\frac{1*2*3*3*4*4*5*5*6*...*13*13*14*14*15*16}{2^2*3^2*...*15^2}$
$=\frac{2*15*16}{2^2*15^2}=\frac{8}{15}$