Question

简便运算 1/1*2+1/2*3+1/3*4+········+1/8*9+1/9*10 快点,好的20分

Answer 1

1/n(n+1)=1/n+1/(n+1)

所以

原式=(1-1/2)+(1/2-1/3)+...+(1/8-1/9)+(1/9-1/10)

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

=1-1/10

=9/10