(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)=?

Making use of the sum of split terms
(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)]
wait a moment