Đáp án: $L=\{2\}$
Giải thích các bước giải:
Ta có:
$(x+\dfrac13)+(x+\dfrac{1}{3.5})+(x+\dfrac{1}{5.7})+...+(x+\dfrac{1}{49.51})=50\dfrac{25}{51}$
$\to (x+\dfrac1{1.3})+(x+\dfrac{1}{3.5})+(x+\dfrac{1}{5.7})+...+(x+\dfrac{1}{49.51})=50\dfrac{25}{51}$
$\to 25x+(\dfrac1{1.3}+\dfrac{1}{3.5})+\dfrac{1}{5.7}+...+\dfrac{1}{49.51})=50\dfrac{25}{51}$
$\to 25x+\dfrac12(\dfrac2{1.3}+\dfrac{2}{3.5})+\dfrac{2}{5.7}+...+\dfrac{2}{49.51})=50\dfrac{25}{51}$
$\to 25x+\dfrac12(\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5})+\dfrac{7-5}{5.7}+...+\dfrac{51-49}{49.51})=50\dfrac{25}{51}$
$\to 25x+\dfrac12(\dfrac11-\dfrac13+\dfrac13-\dfrac15+\dfrac15-\dfrac17+...+\dfrac1{49}-\dfrac1{51})=50\dfrac{25}{51}$
$\to 25x+\dfrac12(\dfrac11-\dfrac{1}{51})=50+\dfrac{25}{51}$
$\to 25x+\dfrac12\cdot \dfrac{50}{51}=50+\dfrac{25}{51}$
$\to 25x+\dfrac{25}{51}=50+\dfrac{25}{51}$
$\to 25x=50$
$\to x=2$
$\to L=\{2\}$
