计算:1∕11×13×15+1∕13×15×17＋…＋1∕29×31×33如题.

Question

计算:1∕11×13×15+1∕13×15×17＋…＋1∕29×31×33
如题.

Answer 1

1/n(n+2)(n+4)=1/4[1/n(n+2)-1/(n+2)(n+4)]
1∕11×13×15+1∕13×15×17＋…＋1∕29×31×33
=1/4*(1/11*13-1/13*15+1/13*15-1/15*17+…＋1∕29*31-1/31*33)
=1/4*(1/11*13-1/31*33)
=1/4*(80/13*31*33)
=20/13299