Question

奥数1/(11×12×13)+1/(12×13×14)+1/(13×14×15)=的解题思路

Answer 1

用拆项法解题。
1/(11×12×13)+1/(12×13×14)+1/(13×14×15)
=1/2*[1/(11*12)-1/(12*13)]+1/2*[1/(12*13)-1/(13*14)]
+1/2*[1/(13*14)-1/(14*15)]
=1/2*[1/(1/11*12)-1/(12*13)+1/(12*13)-1/(13*14)+1/(13*14)-1/(14*15)]
=1/2*[1/(11*12)-1/(14*15)]
=1/2*[1/11-1/12-1/14+1/15]
=1/2*[26/165-26/168]
=13/165-13/168
=(13*56-13*55)/9420
=13/9420 .

Answer 2

先通分：
分母通分成：11*12*13*14*15
分母变成：14*15+11*15+11*12
分母相加约分：答案为：13/9240