a)A=1/1.3+1/3.5+1/5.7+...+1/19.21 b)B=1/99-1/99.98-1/98.97-1/97.96-1/3.2-1/2.1

Đáp án: A = $\frac{10}{21}$ 

              B = $\frac{-97}{99}$

Giải thích các bước giải:

a ) A = $\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + ..... + $\frac{1}{19.21}$ 

2A = $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ + ..... + $\frac{2}{19.21}$ 

2A = 1 - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{5}$ + $\frac{1}{5}$ - $\frac{1}{7}$ +   ..... + $\frac{1}{19}$ -  $\frac{1}{21}$ 

2A = 1 - $\frac{1}{21}$ 

2A = $\frac{20}{21}$ 

A = $\frac{20}{21}$ : 2

A = $\frac{10}{21}$ 

b ) B = $\frac{1}{99}$ - $\frac{1}{99.98}$ - $\frac{1}{98.97}$ - $\frac{1}{97.96}$ - ..... - $\frac{1}{3.2}$ - $\frac{1}{2.1}$ 

B = $\frac{1}{99}$ - ( $\frac{1}{99.98}$ + $\frac{1}{98.97}$ + $\frac{1}{97.96}$ + ..... + $\frac{1}{3.2}$ + $\frac{1}{2.1}$ )

B = $\frac{1}{99}$ - ( $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + ..... + $\frac{1}{96.97}$ + $\frac{1}{97.98}$ + $\frac{1}{98.99}$ )

B = $\frac{1}{99}$ - ( 1 - $\frac{1}{2}$ + $\frac{1}{2}$ - $\frac{1}{3}$ + ..... + $\frac{1}{96}$ - $\frac{1}{97}$ + $\frac{1}{97}$ - $\frac{1}{98}$ + $\frac{1}{98}$ - $\frac{1}{99}$ )

B = $\frac{1}{99}$ - ( 1 - $\frac{1}{99}$ )

B = $\frac{1}{99}$ - $\frac{98}{99}$

B = $\frac{-97}{99}$