Giúp mk câu 20 nhé ai nhanh sẽ được câu trả lời hay nhất

Đáp án:

 `A`

Giải thích các bước giải:

`1/10+1/40+1/88+...+1/340`

`=1/(2xx5)+1/(5xx8)+1/(8xx11)+...+1/(17xx20)`

`=1/3xx(3/(2xx5)+3/(5xx8)+3/(8xx11)+...+3/(17xx20))`

`=1/3xx(1/2-1/5+1/5-1/8+1/8-1/11+...+1/17-1/20)`

`=1/3xx(1/2-1/20)`

`=1/3xx(10/20-1/20)`

`=1/3xx9/20`

`=3/20`

`Đặt` `S` `=` $\dfrac{1}{10}$ `+` $\dfrac{1}{40}$ `+` $\dfrac{1}{88}$ `+` ... `+` $\dfrac{1}{340}$

`S` `xx` `3` `=` $\dfrac{3}{2 \times 5}$ `+` $\dfrac{3}{5 \times 8}$ `+` $\dfrac{3}{8 \times 11}$ `+` ... `+` $\dfrac{3}{17 \times 20}$

`S` `xx` `3` `=` $\dfrac{1}{2}$ `-` $\dfrac{1}{5}$ `+` $\dfrac{1}{5}$ `-` $\dfrac{1}{8}$ `+` ... $\dfrac{1}{17}$ - $\dfrac{1}{20}$

`S` `xx` `3` `=` $\dfrac{1}{2}$ `-` $\dfrac{1}{20}$

`S` `xx` `3` `=` $\dfrac{9}{20}$

`S` `=` $\dfrac{9}{20}$ `:` `3`

`S` `=` $\dfrac{3}{20}$