1/2+1/2÷3+1/3÷4+.+1/9÷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+ --- +1/8-1/9+1/9-1/10
=1-1/10
=9/10