Đáp án:
Giải thích các bước giải:
$A=\dfrac{1}{2^{2}}+\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+...+\dfrac{1}{7^{2}}$
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Ta có: $\dfrac{1}{2^{2}}<\dfrac{1}{1.2}$ ; $\dfrac{1}{3^{2}}<\dfrac{1}{2.3}$ ;...; $\dfrac{1}{7^{2}}<\dfrac{1}{6.7}$
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$⇒\dfrac{1}{2^{2}}+\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+...+\dfrac{1}{7^{2}}<\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{6.7}$
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$⇒\dfrac{1}{2^{2}}+\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+...+\dfrac{1}{7^{2}}<1-\dfrac{1}{7}$
$ $
$⇒\dfrac{1}{2^{2}}+\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+...+\dfrac{1}{7^{2}}<\dfrac{6}{7}<1$
$ $
$⇒\dfrac{1}{2^{2}}+\dfrac{1}{3^{2}}+\dfrac{1}{4^{2}}+...+\dfrac{1}{7^{2}}<1$
