(1-2\1)*(1+2\1)*(1-3\1)*(1+3\1)*(1-4\1)*(1+4\1)*.....*(1-99\1)*(1+99\1)

(1-2\1)*(1+2\1)*(1-3\1)*(1+3\1)*(1-4\1)*(1+4\1)*.....*(1-99\1)*(1+99\1)
=(1-1/2^2)(1-1/3^2)*..*(1-1/99^2)

1-1/n^2=(n^2-1)/n^2=(n+1)*(n-1)/n^2

(1-2\1)*(1+2\1)*(1-3\1)*(1+3\1)*(1-4\1)*(1+4\1)*.....*(1-99\1)*(1+99\1)
=(1-1/2^2)(1-1/3^2)*..*(1-1/99^2)
=(1*3/2^2)*(2*4/3^2)*...*(98*100/99^2)
分子=1*3*(2*4)*(3*5)*...*(98*100)=(1*2*..*98)*(3*4*...*100)
分母=2*2*3*3*..*99*99=(2*3*...*99)*(2*3*...*99)

相除得到：(1-2\1)*(1+2\1)*(1-3\1)*(1+3\1)*(1-4\1)*(1+4\1)*.....*(1-99\1)*(1+99\1)
=(1-1/2^2)(1-1/3^2)*..*(1-1/99^2)
=(1*3/2^2)*(2*4/3^2)*...*(98*100/99^2)
=(1*2*..*98)*(3*4*...*100)/[(2*3*...*99)*(2*3*...*99]
=（1*100）/（99*2）
=50/99