Giúp tôi bài này……….

Đáp án:

Giải thích các bước giải:

d)

$A$ $=$ $\dfrac{1}{1×3}$ $+$ $\dfrac{1}{3×5}$ $+$ $\dfrac{1}{5×7}$ $+$ ...... $+$ $\dfrac{1}{2019×2021}$ $+$ $\dfrac{1}{2021×2023}$

$A$ $×$ $2$ $=$ $($ $\dfrac{1}{1×3}$ $+$ $\dfrac{1}{3×5}$ $+$ $\dfrac{1}{5×7}$ $+$ ...... $+$ $\dfrac{1}{2019×2021}$ $+$ $\dfrac{1}{2021×2023}$ $)$  $×$ $2$ 

$A$ $×$ $2$ $=$ $\dfrac{2}{1×3}$ $+$ $\dfrac{2}{3×5}$ $+$ $\dfrac{2}{5×7}$ $+$ ...... $+$ $\dfrac{2}{2019×2021}$ $+$ $\dfrac{2}{2021×2023}$ 

$A$ $×$ $2$ $=$ $1$ $-$ $\dfrac{1}{3}$ $+$ $\dfrac{1}{3}$ $-$ $\dfrac{1}{5}$ $+$ ..... $+$ $\dfrac{1}{2019}$ $-$ $\dfrac{1}{2021}$ $+$ $\dfrac{1}{2021}$ $-$ $\dfrac{1}{2023}$

$A$ $×$ $2$ $=$ $1$ $-$ $\dfrac{1}{2023}$

$A$ $×$ $2$ $=$ $\dfrac{2022}{2023}$ 

$A$ $=$ $\dfrac{2022}{2023}$ $:$ $2$ $=$ $\dfrac{1011}{2023}$ 

d)

$A$ $=$ $\dfrac{5}{1×3}$ $+$ $\dfrac{5}{3×5}$ $+$ $\dfrac{5}{5×7}$ $+$ ...... $+$ $\dfrac{5}{2019×2021}$ $+$ $\dfrac{5}{2021×2023}$

$A$  $=$ $($ $\dfrac{1}{1×3}$ $+$ $\dfrac{1}{3×5}$ $+$ $\dfrac{1}{5×7}$ $+$ ...... $+$ $\dfrac{1}{2019×2021}$ $+$ $\dfrac{1}{2021×2023}$ $)$  $×$ $5$

$A$  $=$ $\dfrac{1011}{2023}$ $×$ $5$

$A$ $=$ $\dfrac{5055}{2023}$