Đáp án:
Giải thích các bước giải:
$A=\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+\dfrac{1}{5^{2}}+...+\dfrac{1}{100}$
$ $
$A=\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+\dfrac{1}{5^{2}}+...+\dfrac{1}{10^{2}}$
$ $
$⇒A=\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+\dfrac{1}{5^{2}}+...+\dfrac{1}{10^{2}}<\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{9.10}$
$ $
$⇒A=\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+\dfrac{1}{5^{2}}+...+\dfrac{1}{10^{2}}<\dfrac{1}{2}-\dfrac{1}{10}<\dfrac{1}{2}$
$ $
$⇒A=\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+\dfrac{1}{5^{2}}+...+\dfrac{1}{10^{2}}<\dfrac{1}{2}$
$ $
$\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+\dfrac{1}{5^{2}}+...+\dfrac{1}{100}<\dfrac{1}{2}$
