Giải thích các bước giải:
Ta có:
$\dfrac1{4^2}+\dfrac1{5^2}+...+\dfrac1{60^2}$
$=\dfrac1{4.4}+\dfrac1{5.5}+...+\dfrac1{60.60}$
$<\dfrac1{3.4}+\dfrac1{4.5}+...+\dfrac1{59.60}$
$<\dfrac{4-3}{3.4}+\dfrac{5-4}{4.5}+...+\dfrac{60-59}{59.60}$
$<\dfrac13-\dfrac14+\dfrac14-\dfrac15+...+\dfrac1{59}-\dfrac1{60}$
$<\dfrac13-\dfrac1{60}$
$<\dfrac13$
$\to \dfrac1{4^2}+\dfrac1{5^2}+...+\dfrac1{60^2}<\dfrac13$
$\to\dfrac1{3^2}+ \dfrac1{4^2}+\dfrac1{5^2}+...+\dfrac1{60^2}<\dfrac1{3^2}+\dfrac13$
$\to\dfrac1{3^2}+ \dfrac1{4^2}+\dfrac1{5^2}+...+\dfrac1{60^2}<\dfrac49$
$\to đpcm$
