Question

Tinh nhanh

A=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10

Answer 1

A=1/1*2+1/2*3+...+1/9*10

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

=(1-1/10)+(1/2-1/2)+...+(1/9-1/9)

=(10/10-1/10)+0+...+0=9/10

Answer 2

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}=1-\frac{1}{10}=\frac{9}{10}\)