JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Multinomial theorem, Terms free from radical sign in the expansion(a1/p+b1/q), Problems regarding to three four consecutive terms or coefficients

  • question_answer
    If in the expansion of \[{{(1+x)}^{n}}\], a, b, c are three consecutive coefficients, then n=

    A) \[\frac{ac+ab+bc}{{{b}^{2}}+ac}\]

    B) \[\frac{2ac+ab+bc}{{{b}^{2}}-ac}\]

    C) \[\frac{ab+ac}{{{b}^{2}}-ac}\]

    D) None of these

    Correct Answer: B

    Solution :

    Trick: Here\[a={{\,}^{n}}{{C}_{r}},\,\,b={{\,}^{n}}{{C}_{r+1}}\]and \[c={{\,}^{n}}{{C}_{r+2}}\] Put\[n=2,r=0\], then option (b) holds the condition i.e. \[n=\frac{2ac+ab+bc}{{{b}^{2}}-ac}\]


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