1/1*2=1-1/21/2*3=1/2-1/31/3*4=1/3-1/4.1/39*40=1/39-1/40∴1/1*2+1/2*3+1/3*4+1/4*5+.1/39*40=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-.1/39+1/39-1/40=1-1/40=39/40