1/(12*13)+1/(13*14)+1/(14*15)+1/(15*16)+1/(16*17)+1/(17*18)+

題目：

1/(12*13)+1/(13*14)+1/(14*15)+1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)=?

解答：

1/a(a+1)=1/a-1/(a+1)
1/(12*13)+1/(13*14)+1/(14*15)+1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)
=1/12-1/13+1/13-1/14+1/14-1/15+……+1/19-1/12
=1/12-1/20
=5/60-3/60
=2/60
=1/15