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  • 题型:选择题 题类:期中考试 难易度:中档

    下面给出的类比推理中,结论正确的有\((\:\:\:\:)\)
    ①若数列\(\{a _{n} \}\)是等差数列,\(b _{n} = \dfrac {1}{n} (a _{1} +a _{2} +…+a _{n} )\),则数列\(\{b _{n} \}\)也是等差数列;类比推出:若数列\(\{c _{n} \}\)是各项都为正数的等比数列,\(d _{n} = \sqrt[n]{c_{1}c_{2}\cdots c_{n}}\),则数列\(\{d _{n} \}\)也是等比数列;
    ②\(a\),\(b\)为实数,若\(a ^{2} +b ^{2} =0\),则\(a=b=0\);类比推出:\(z _{1}\),\(z _{2}\)为复数,若\(z _{1} ^{2} +z _{2} ^{2} =0\),则\(z _{1} =z _{2} =0\);
    ③若\(a\),\(b\),\(c∈R\),则\((ab)c=a(bc)\);类比推出:若\( \overrightarrow {a}, \overrightarrow {b}, \overrightarrow {c}\)为三个向量,则\(( \overrightarrow {a}\cdot \overrightarrow {b}) \overrightarrow {c}= \overrightarrow {a}\cdot ( \overrightarrow {b}\cdot \overrightarrow {c})\);
    ④在平面内,三角形的两边之和大于第三边;类比推出:在空间中,四面体的任意三个面的面积之和大于第四个面的面积;
    ⑤若三角形周长为\(l\),面积为\(S\),则其内切圆半径\(r= \dfrac {2S}{l}\);类比推出:若三棱锥表面积为\(S\),体积为\(V\),则其内切球半径\(r= \dfrac {3V}{S}\).
    A. ①②③ B. ①④ C. ③④⑤ D. ①④⑤
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