((1+1\2)(1+1\3)(1+1\4)(1+1\5)------(1+1\100))\(1-1\2)(1-1\3)(1-1\4)------(1-1\100)等多少

来源：百度知道 编辑：UC知道 时间：2024/05/17 01:06:36

((1+1\2)(1+1\3)(1+1\4)(1+1\5)------(1+1\100))\(1-1\2)(1-1\3)(1-1\4)------(1-1\100)
=((3/2)*(4/3)*(5/4)*...*101/100)/((1/2)*(2/3)*...*(99/100))
=(101/2)/(1/100)
=101*50
=5050

分子式子=3\2*4\3*5\4*6\5*7\6……101\100=101\2
分母式子=1\2*2\3*3\4*4\5*5\6……99\100=1\100
故结果为50*101=5050

(1+1\2)(1+1\3)(1+1\4)(1+1\5)……(1+1\100))\(1-1\2)(1-1\3)(1-1\4)……(1-1\100)
=((3/2)*(4/3)*(5/4)*……*101/100)/((1/2)*(2/3)*……*(99/100))
=(101/2)/(1/100)
=101*50
=5050