Ta có:
$\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+\dfrac{1}{25}+..+\dfrac{1}{10000}$
$=\dfrac{1}{2\times2}+\dfrac{1}{3\times3}+\dfrac{1}{4\times4}+\dfrac{1}{5\times5}+..+\dfrac{1}{100\times100}$
$<\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+..+\dfrac{1}{99\times100}$
$=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+..+\dfrac{1}{99}-\dfrac{1}{100}$
$=1-\dfrac{1}{100}$
$=\dfrac{99}{100}<1$
Vậy điền dấu $<$
