Giải thích các bước giải:
Ta có :
$A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}$
$\to A=\dfrac{1}{2.2}+\dfrac{1}{3.3}+\dfrac{1}{4.4}+\dfrac{1}{5.5}+\dfrac{1}{6.6}+\dfrac{1}{7.7}$
$\to A<\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}$
$\to A<\dfrac{2-1}{1.2}+\dfrac{3-2}{2.3}+\dfrac{4-3}{3.4}+\dfrac{5-4}{4.5}+\dfrac{6-5}{5.6}+\dfrac{7-6}{6.7}$
$\to A<\dfrac11-\dfrac12+\dfrac12-\dfrac13+\dfrac13-\dfrac14+\dfrac14-\dfrac15+\dfrac15-\dfrac16+\dfrac16-\dfrac17$
$\to A<1-\dfrac17$
$\to A<1$
