Đáp án:
Giải thích các bước giải:
Ta có:
$\dfrac{4^{2}}{20.24}+\dfrac{4^{2}}{24.28}+...+\dfrac{4^{2}}{76.80}<\dfrac{4}{20.24}+\dfrac{4}{24.28}+...+\dfrac{4}{76.80}$
$ $
$\dfrac{4}{20.24}+\dfrac{4}{24.28}+...+\dfrac{4}{76.80}$
$ $
$=\dfrac{1}{20}-\dfrac{1}{24}+\dfrac{1}{24}-\dfrac{1}{28}+...+\dfrac{1}{76}-\dfrac{1}{80}$
$ $
$=\dfrac{1}{20}-\dfrac{1}{80}$
$ $
$=\dfrac{3}{80}<1$
$ $
$⇒\dfrac{4^{2}}{20.24}+\dfrac{4^{2}}{24.28}+...+\dfrac{4^{2}}{76.80}<\dfrac{4}{20.24}+\dfrac{4}{24.28}+...+\dfrac{4}{76.80}<1$
$ $
$⇒\dfrac{4^{2}}{20.24}+\dfrac{4^{2}}{24.28}+...+\dfrac{4^{2}}{76.80}<1$
