1/2+1/6+1/12+......+1/1980+1/2070=?

来源：百度知道 编辑：UC知道 时间：2024/05/13 04:50:56
要写步奏

1/2+1/6+1/12+......+1/1980+1/2070
=1-1/2+1/2-1/3+1/3-1/4+......1/44-1/45+1/45-1/46
=1-1/46=45/46

这些数有什么规律？
………………

好吧。。。算我没看出来= =

1/2+1/6+1/12+......+1/1980+1/2070
=1/(1*2)+1/(2*3)+1/(3*4)...+1/(44*45)+1/(45*46)
=1-1/2+1/2-1/3+1/3-1/4...+1/44-1/45+1/45-1/46
=1-1/46
=45/46

1/2+1/6+1/12+......+1/1980+1/2070
=1/(1*2)+1/(2*3)+1/(3*4)...+1/(44*45)+1/(45*46)
=1-1/2+1/2-1/3+1/3-1/4...+1/44-1/45+1/45-1/46
=1-1/46
=45/46
因为1/N*(N=1)可以写成1/N-1/(N=1)

1/2+1/6+1/12+......+1/1980+1/2070
=1/(1*2)+1/(2*3)+1/(3*4)...+1/(44*45)+1/(45*46)
=1-1/2+1/2-1/3+1/3-1/4...+1/44-1/45+1/45-1/46
=1-1/46
=45/46
就是这个答案