Question

1/1×3＋1/3×5＋1/5×7＋1/7×9＋1/9×11＋……＋1/19×21

用简便方法计算

Answer 1

1/1×3＋1/3×5＋1/5×7＋1/7×9＋1/9×11＋……＋1/19×21
=(1/2)(1/1-1/3+1/3-1/5+...+1/19-1/21)
=(1/2)(1-1/21)
=10/21

把每一个都拆成两项相减
比如1/1×3=(1/1-1/3)/2

Answer 2

答案:10/21
利用 1/[(n-1)*(n+1)]=(1/2)*{[1/(n-1)]-[1/(n+1)]}
原式=(1/2)*(1-1/3+1/3-1/5+1/5-1/7+……-1/19+1/21)
=10/21

Answer 3

1/1×3＋1/3×5＋1/5×7＋1/7×9＋1/9×11＋……＋1/19×21
=(1/2)(2/1×3＋2/3×5＋……＋1/19×21)
=(1/2)(1/1-1/3+1/3-1/5+……＋1/19-1/21)
=(1/2)(1/1-1/21)
=10/21