\(A-1=\frac{1}{1.2}+\frac{1}{2.3}..+\frac{1}{99.100}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+..+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}\)\(=\frac{99}{100}\)
\(A=1+\frac{99}{100}=\frac{199}{100}\)
=1+1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100
=1+1/2+1/2-1/100
=199/100
A=1+1/2+1/2.3+1/3.4+...+1/98.99+1/99.100
A=1+1/1-1/2+1/2-1/3+1/4+...+1/98-1/99+1/99-1/100
A-1=1-1/100
A-1=99/100
A=99/100+1
A=199/100
Vậy A=199/100
Đặt biểu thức là A.
Ta có: A - 1=1/1.2+1/2.3+1/3.4+...+1/99.100
=>A-1= 1/1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
=>A-1=1/1-1/100
=>A-1=99/100
=>A=99/100+1
=>A=199/100.
