很简单的数学题，请问谁有最简单的办法解决

=(1＋1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/100)(1-1/100)
=[(1+1/2)(1+1/3)……(1+1/100)][(1-1/2)(1-1/3)……(1-1/100)]
=[(3/2)*(4/3)*……*(101/100)][(1/2)*(2/3)*……*(99/100)]
=(101/2)*(1/100)
=101/200

101/200
（1-1/2²）=(2+1)(2-1)/2²
同理 1-1/1-1/3²=（3+1)(3-1)/1-1/3²
所以原式=1*2*3……*99*3*4*……*100*101/2²*3²---100²
化简相消得101/200

真的饿~