Làm nhanh nha cảm ơn

Đáp án:

$L$={$2$}

Giải thích các bước giải:

$\left({x+\dfrac{1}{3}}\right)+\left({x+\dfrac{1}{3.5}}\right)+..+\left({x+\dfrac{1}{49.51}}\right)=50+\dfrac{25}{51}$
$⇔25x+\dfrac{1}{2}\left({1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+..+\dfrac{1}{49}-\dfrac{1}{51}}\right)=50+\dfrac{25}{51}$
$⇔25x+\dfrac{1}{2}\left({1-\dfrac{1}{51}}\right)=50+\dfrac{25}{51}$
$⇔25x+\dfrac{25}{51}=50+\dfrac{25}{51}$
$⇔25x=50$
$⇔x=2$ (thoả mãn $x∈N$)
Vậy $L$={$2$}