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

来源：学生作业帮助网编辑：作业帮时间：2024/10/05 02:42:59

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

(n+1)(n+2)/1 +(n+2)(n+3)/1 +(n+3)(n+4)/1
(n+1)(n+2)/1 +(n+2)(n+3)/1 +(n+3)(n+4)/1
=(n+1)(n+2) +(n+2)(n+3) +(n+3)(n+4)
=(n+2)(n+1+n+3)+n^2+7n+12
=(n+2)(2n+4)+n^2+7n+12
=2(n+2)^2+n^2+7n+12
=2(n^2+4n+4)+n^2+7n+12
=3n^2+15n+20

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

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