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JEE Main & Advanced Mathematics Sequence & Series Question Bank Self Evaluation Test - Sequences and Series

  • question_answer
    If a, b, c are positive numbers, then least value of\[(a+b+c)\left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right)\] is

    A) 1

    B) 6   

    C) 9

    D) None

    Correct Answer: C

    Solution :

    [c] \[AM\ge HM\] \[\Rightarrow \,\frac{a+b+c}{3}\ge \frac{3}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}\] \[\Rightarrow \,(a+b+c)\left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right)\ge 9\]


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