Giải thích các bước giải:
Xét biểu thức:
`2/(n(n+1)(n+2))`
`=(-(n+2)+n)/(n(n+1)(n+2))`
`=-(n+2)/(n(n+1)(n+2))+n/(n(n+1)(n+2))`
`=-1/(n(n+1))+1/((n+1)(n+2))`
$\Rightarrow A=\dfrac{1}{1. 2. 3}+\dfrac{1}{2. 3. 4}+\dfrac{1}{3. 4. 5}+...+\dfrac{1}{18. 19. 20}\\\Rightarrow 2A=\dfrac{2}{1. 2. 3}+\dfrac{2}{2. 3. 4}+\dfrac{2}{3. 4. 5}+...+\dfrac{2}{18. 19. 20}\\\Rightarrow 2A=-\dfrac{1}{1. 2}+\dfrac{1}{2. 3}-\dfrac{1}{2. 3}+\dfrac{1}{3. 4}-\dfrac{1}{3. 4}+\dfrac{1}{4. 5}-...-\dfrac{1}{18. 19}+\dfrac{1}{19. 20}\\\Rightarrow 2A=-\dfrac{1}{2}+\dfrac{1}{19. 20}\\\Rightarrow 2A=-\dfrac{189}{380}\\\Rightarrow A=-\dfrac{189}{760}$
