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Math Help - ! - Binomial Theorem - Expanding Terms question

  1. #1
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    ! - Binomial Theorem - Expanding Terms question

    34. The first three terms in the expansion of (1 + ay)^n are 1, 12y and 68y^2.

    Evaluate a and n. Use the fact that...

    (1 + ay)^n = 1 + nay + n(n-1) 2 (ay)^2 + ...


    Any help in evaluating 'a' and 'n' would be GREATLY appreciated!
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    Quote Originally Posted by cnmath16 View Post
    34. The first three terms in the expansion of (1 + ay)^n are 1, 12y and 68y^2.

    Evaluate a and n. Use the fact that...

    (1 + ay)^n = 1 + nay + n(n-1) 2 (ay)^2 + ...


    Any help in evaluating 'a' and 'n' would be GREATLY appreciated!
    Coefficient of y: 12 = na .... (1)

    Coefficient of y^2: \frac{n(n-1)}{2} \, a^2 = 68 \Rightarrow n(n-1) a^2 = 136 .... (2)

    Now solve equations (1) and (2) simultaneously. Hint: Note that when you square equation (1) you get 144 = n^2 a^2.
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