Giải thích các bước giải:
Ta có :
$B=\dfrac{5^2}{10^2}+\dfrac{5^2}{11^2}+\dfrac{5^2}{12^2}+....+\dfrac{5^2}{99^2}$
$\to B=5^2(\dfrac{1}{10^2}+\dfrac{1}{11^2}+\dfrac{1}{12^2}+....+\dfrac{1}{99^2})$
$\to B=25(\dfrac{1}{10.10}+\dfrac{1}{11.11}+\dfrac{1}{12.12}+...+\dfrac{1}{99.99})$
$\to B>25(\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}+...+\dfrac{1}{99.100})$
$\to B>25(\dfrac{11-10}{10.11}+\dfrac{12-11}{11.12}+\dfrac{13-12}{12.13}+....+\dfrac{100-99}{99.100})$
$\to B>25(\dfrac1{10}-\dfrac{1}{11}+\dfrac1{11}-\dfrac1{12}+\dfrac1{12}-\dfrac1{13}+....+\dfrac1{99}-\dfrac1{100})$
$\to B>25(\dfrac1{10}-\dfrac1{100})$
$\to B>25\cdot \dfrac{9}{100}$
$\to B>\dfrac94$
