Question

1/1*2+1/2*3+1/3*4+···1/8*9+1/9*10简便计算

Answer 1

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