1/(1*2)-1/(2*3)-1/(3*4)...-1/(9*10)=(1/1 - 1/2)-(1/2 - 1/3)-(1/3 - 1/4)...-(1/9 - 1/10)=1/1 - 1/2 - 1/2 + 1/3 - 1/3 + 1/4 - 1/4 ...-1/9 + 1/10 = 1/1 - 1/2 - 1/2 + (1/3 - 1/3 + 1/4 - 1/4 ...+ 1/9 - 1/9) + 1/10=1/10
1/(1*2)-1/(2*3)-1/(3*4)...-1/(9*10)=(1/1 - 1/2)-(1/2 - 1/3)-(1/3 - 1/4)...-(1/9 - 1/10)=1/1 - 1/2 - 1/2 + 1/3 - 1/3 + 1/4 - 1/4 ...-1/9 + 1/10 = 1/1 - 1/2 - 1/2 + (1/3 - 1/3 + 1/4 - 1/4 ...+ 1/9 - 1/9) + 1/10=1/10