Question

Tính hiệu A-B

A=1/(1×2)+1/(3×4)+...+1/(99×100)

B=1/50+1/51+1/52+...+1/99+1/100

Answer 1

B=1/1.2+1/3.4+1/5.6+...+1/99.100 

=1‐1/2+1/3‐1/4+1/5‐1/6+...+1/99‐1/100 

=﴾1+1/3+1/5+...+1/99﴿‐﴾1/2+1/4+1/6+...+1/100﴿ 

=﴾1+1/2+1/3+1/4+1/5+1/6+...+1/99+1/100﴿‐2﴾1/2+1/4+1/6+...+1/100﴿ 

=﴾1+1/2+1/3+1/4+...+1/100﴿‐﴾1+1/2+1/3+..+1/50﴿ 

=1/51+1/52+1/53+..+1/100 ﴾1﴿ 

A=1/51+1/52+1/53+..+1/100 ﴾2﴿ 

Từ ﴾1﴿,﴾2﴿=> A-B=0