1/1*2+1/2*3+1/3*4+···1/8*9+1/9*10
=(2-1)/1*2+(3-2)/2*3+(4-3)/3*4+···(9-8)/8*9+(10-9)/9*10
=1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9+1/9-1/10
=1-1/10
=9/10