(1/1*4)+(1/2*5)+(1/3*6)…+(1/17*20)+(1/18*21)=?

(1/1*4)+(1/2*5)+(1/3*6)…+(1/17*20)+(1/18*21)=?

利用裂項求和法做
(1/1*4)+(1/2*5)+(1/3*6)…+(1/17*20)+(1/18*21)
=(1/3)×(1-1/4+1/2-1/5+1/3-1/6……+1/17-1/20+1/18-1/21)
=(1/3)×(1+1/2+1/3+……1/18)-(1/4+1/5+1/6+……1/21)
=(1/3)×[(1+1/2+1/3)-(1/19+1/20+1/21)]
稍等