A=1/1x3+1/3x5+1/5x7+...+1/97x99

Đáp án:

$\dfrac{49}{99}$

Giải thích các bước giải:

`A =` $\dfrac{1}{1. 3}$ + $\dfrac{1}{3. 5}$ + $\dfrac{1}{5. 7}$ `+ ...+` $\dfrac{1}{97. 99}$
`=` $\dfrac{1}{2}$`.` ($\dfrac{2}{1. 3}$ + $\dfrac{2}{3. 5}$ `+...+` $\dfrac{2}{97. 99}$)
`=` $\dfrac{1}{2}$`.` ( `1` `-` $\dfrac{1}{3}$ `+ ` $\dfrac{1}{3}$ `-` $\dfrac{1}{5}$ `+ ...+` $\dfrac{1}{97}$ `-` $\dfrac{1}{99}$)
`=` $\dfrac{1}{2}$`.` ( `1 - ` $\dfrac{1}{99}$)
`=` $\dfrac{1}{2}$`.` $\dfrac{98}{99}$
`=` $\dfrac{49}{99}$

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