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Math Help - Binomial question

  1. #1
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    Binomial question

    i) Find the coeficient of 1/x⁵ in the expansion of (2x + 1/x)
    ii) Find the term which is independant of x in the expansion of (x - 1/x)

    im in grade 11 and have an exam in 3 days. I tried to do them but get stuck or get a totally wrong answer!
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    Quote Originally Posted by milan View Post
    i) Find the coeficient of 1/x⁵ in the expansion of (2x + 1/x)
    Let's expand using Newton's binomial theorem : \left(2x+\frac{1}{x}\right)^7=\sum_{k=0}^7\binom{7  }{k}(2x)^k\left(\frac{1}{x}\right)^{7-k}=\sum_{k=0}^7\binom{7}{k}2^k \underbrace{x^k}_{\frac{1}{x^{-k}}} \frac{1}{x^{7-k}}=\sum_{k=0}^7\binom{7}{k}2^k\frac{1}{x^{7-2k}}

    The coefficient of \frac{1}{x^5} is  \binom{7}{k}2^k for k such that \frac{1}{x^{7-2k}}=\frac{1}{x^5} \Leftrightarrow 7-2k=5
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