Giải thích các bước giải:
Ta có :
$A=\dfrac{1}{5^2}+\dfrac{1}{6^2}+..+\dfrac{1}{100^2}$
$\to A=\dfrac{1}{5.5}+\dfrac{1}{6.6}+..+\dfrac{1}{100.100}$
$\to \dfrac{1}{5.6}+\dfrac{1}{6.7}+..+\dfrac{1}{100.101}<A<\dfrac{1}{4.5}+\dfrac{1}{5.6}+..+\dfrac{1}{99.100}$
$\to \dfrac{6-5}{5.6}+\dfrac{7-6}{6.7}+..+\dfrac{101-100}{100.101}<A<\dfrac{5-4}{4.5}+\dfrac{6-5}{5.6}+..+\dfrac{100-99}{99.100}$
$\to\dfrac 15-\dfrac 16+\dfrac 16-\dfrac 17+..+\dfrac{1}{100}-\dfrac{1}{101}<A<\dfrac 14-\dfrac 15+..+\dfrac{1}{99}-\dfrac{1}{100}$
$\to \dfrac 15-\dfrac{1}{101}<A<\dfrac 14-\dfrac{1}{100}$
$\to \dfrac 15-\dfrac{1}{30}<A<\dfrac 14$
$\to \dfrac 16<A<\dfrac 14$
