1/3X1/4十1/4X1/5十1/5X1/6十1/6……1/47X1/48等于多少？

Question

如题所述

Answer 1

1/3X1/4十1/4X1/5十1/5X1/6十1/6……1/47X1/48
=1/3-1/4+1/4-1/5+...+1/47-1/48
=1/3-1/48
=16/48-1/48
=15/48
=5/16;追答

1/3X1/4十1/4X1/5十1/5X1/6十1/6……1/47X1/48
=1/3-1/4+1/4-1/5+...+1/47-1/48
=1/3-1/48
=16/48-1/48
=15/48
=5/16;

1/3X1/4十1/4X1/5十1/5X1/6十1/6……1/47X1/48
=1/3-1/4+1/4-1/5+...+1/47-1/48
=1/3-1/48
=16/48-1/48
=15/48
=5/16;

追问

不对吧

为什么乘变成减了

追答

对的啊；
裂项法：1/n×(n+1)=1/n-1/(n+1);
中间相互抵消了，最后剩余
1/3-1/48
=16/48-1/48
=15/48
=5/16;

对的啊；
裂项法：1/n×(n+1)=1/n-1/(n+1);
中间相互抵消了，最后剩余
1/3-1/48
=16/48-1/48
=15/48
=5/16;

追问

谢谢

追答

希望好评，谢谢