计算:x(x+1)分之1(x+1)(x+2)分之1+...(x+2012)(x+2013)分之1

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 16:48:29
计算:x(x+1)分之1(x+1)(x+2)分之1+...(x+2012)(x+2013)分之1

计算:x(x+1)分之1(x+1)(x+2)分之1+...(x+2012)(x+2013)分之1
计算:x(x+1)分之1(x+1)(x+2)分之1+...(x+2012)(x+2013)分之1

计算:x(x+1)分之1(x+1)(x+2)分之1+...(x+2012)(x+2013)分之1
x(x+1)分之1+(x+1)(x+2)分之1+...(x+2012)(x+2013)分之1
=1/x-1/(x+1)+1/(x+1)-1/(x-2)+.+1/(x+2012)-1/(x+2013)
=1/x-1/(x+2013)
=(x+2013)/x(x+2013)-x/x(x+2013)
=2013/x(x+2013)

x(x+1)分之1+(x+1)(x+2)分之1+... (x+2012)(x+2013)分之1
=1/x-1/(x+1)+1/(x+1)-1/(x-2)+....+1/(x+2012)-1/(x+2013)
=1/x-1/(x+2013)
=(x+2013)/x(x+2013)-x/x(x+2013)
=2013/x(x+2013)