Question

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

Answer 1

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