计算1/x(x+1).+1/(x+199)(x+200)

来源：学生作业帮助网编辑：作业帮时间：2024/05/10 18:04:34

计算1/x(x+1).+1/(x+199)(x+200)
计算1/x(x+1).+1/(x+199)(x+200)

计算1/x(x+1).+1/(x+199)(x+200)
1/x(x+1).+1/(x+199)(x+200)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+199)-1/(x+200)
=1/x-1/(x+200)
=200/x(x+200)
就是一个加一个减一个的过程

原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+..........1/(x+199)-1/(x+200)
=1/x-1/(x+200)
=200/[x*(x+200)]

1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)……+1/(x+199)-1/(x+200)=1/x-1/(x+200)

1/x(x+1)....+1/(x+199)(x+200)
=1/x-1/(x+200)
=200/ (x^2+200x)

=1/x-1/(x+1)+1/(x+1)-1/(x+2)+......1/(x+199)-1/(x+200)=1/x-1/(x+200)

1/x(x+1)=1/x-1/(x+1) 1/(x+1)(x+2)=1/(x+1)-1/(x+2) ........ 1/(x+199)(x+200)=1/(x+199)-1/(x+200)
都相互抵消，可得出答案为1/x-1/(x+200)

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