(n+1)(n+2)分之1 +(n+2)(n+3)分之1 +(n+3)(n+4)分之1

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 11:47:43
(n+1)(n+2)分之1+(n+2)(n+3)分之1+(n+3)(n+4)分之1(n+1)(n+2)分之1+(n+2)(n+3)分之1+(n+3)(n+4)分之1(n+1)(n+2)分之1+(n+2

(n+1)(n+2)分之1 +(n+2)(n+3)分之1 +(n+3)(n+4)分之1
(n+1)(n+2)分之1 +(n+2)(n+3)分之1 +(n+3)(n+4)分之1

(n+1)(n+2)分之1 +(n+2)(n+3)分之1 +(n+3)(n+4)分之1
(n+1)(n+2)分之1 +(n+2)(n+3)分之1 +(n+3)(n+4)分之1
=1/(n+1)(n+2)+1/(n+2)(n+3)+1/(n+3)(n+4)
=1/n+1-1/n+2+1/n+2-1/n+3+1/n+3-1/n+4
=1/n+1-1/n+4
=(n+4-n-1)/(n+4)(n+1)
=3/(n+4)(n+1)

(n+1)(n+2)分之1 +(n+2)(n+3)分之1 +(n+3)(n+4)分之1
=1/(n+1)-1/(n+2)+1/(n+2)-1/(n+3)+1/(n+3)-1/(n+4)
=1/(n+1)-1/(n+4)
=3/(n+1)(n+4)

原式=1/(n+1)-1/(n+2)+1/(n+2)-1/(n+3)+1/(n+3)-1/(n+4)=1/(n+1)-1/(n+4)