优优班--学霸训练营 > 题目详情
  • 先观察下列等式,再回答下列问题:
    \(① \sqrt {1+ \dfrac {1}{1^{2}}+ \dfrac {1}{2^{2}}}=1+ \dfrac {1}{1}- \dfrac {1}{1+1}=1 \dfrac {1}{2}\);  \(② \sqrt {1+ \dfrac {1}{2^{2}}+ \dfrac {1}{3^{2}}}=1+ \dfrac {1}{2}- \dfrac {1}{2+1}=1 \dfrac {1}{6}\)
    \(③ \sqrt {1+ \dfrac {1}{3^{2}}+ \dfrac {1}{4^{2}}}=1+ \dfrac {1}{3}- \dfrac {1}{3+1}=1 \dfrac {1}{12}\)
    \((1)\)请你根据上面三个等式提供的信息,猜想\( \sqrt {1+ \dfrac {1}{4^{2}}+ \dfrac {1}{5^{2}}}\)的结果,并验证;
    \((2)\)请你按照上面各等式反映的规律,用含\(n\)的等式表示\((n\)为正整数\()\).
    【考点】算术平方根,数字字母规律问题
    【分析】请登陆后查看
    【解答】请登陆后查看
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