Question

求（1-1/2^2)*(1-1/3^)*(1-1/4^)*……*（1-1/99^2)*(1-1/100^2)的值

Answer 1

（1-1/2^2)*(1-1/3^)*(1-1/4^)*……*（1-1/99^2)*(1-1/100^2)

=(1-1/2)(1+1/2)(1-1/3)(1+1/3)*.（1-1/99）(1+1/99)(1-1/100)(1+1/100)

=(1/2)*(3/2)(2/3)*(4/3)*.(98/99)*(100/99)(99/100)(101/100)

=(1/2)*(101/100)

=101/200

提示：运用平方差公式