Giải thích các bước giải:
Ta có:
$E=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}$
$\to E=\dfrac{1}{2\cdot2}+\dfrac{1}{3\cdot3}+\dfrac{1}{4\cdot4}+...+\dfrac{1}{100\cdot100}$
$\to E<\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}$
$\to E<\dfrac{2-1}{1\cdot2}+\dfrac{3-2}{2\cdot3}+\dfrac{4-3}{3\cdot4}+...+\dfrac{100-99}{99\cdot100}$
$\to E<\dfrac11-\dfrac12+\dfrac12-\dfrac13+\dfrac13-\dfrac14+...+\dfrac1{99}-\dfrac1{100}$
$\to E<1-\dfrac1{100}<1$
$\to E<1$
