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Math Help - Find the 12th term in the expansion (5x+2)^14?

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    Find the 12th term in the expansion (5x+2)^14?

    Find the 12th term in the expansion (5x+2)^14
    I did (14 ncr 11) (5x)^3 (2)^11
    364 (125x^3) (2048)
    93,184,000x^3. Is that right?
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    Quote Originally Posted by rowdy3 View Post
    I did (14 ncr 11) (5x)^3 (2)^11
    Looks fine to me.
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    Quote Originally Posted by rowdy3 View Post
    Find the 12th term in the expansion (5x+2)^14
    I did (14 ncr 11) (5x)^3 (2)^11
    364 (125x^3) (2048)
    93,184,000x^3. Is that right?

    This can be tricky: you can both write (5x+2)^{14}=\displaystyle{\sum\limits^{14}_{k=0}\b  inom{14}{k}(5x)^{14-k}2^k=\sum\limits^{14}_{k=0}\binom{14}{k}(5x)^{k}2  ^{14-k}}

    In the first case you obtain \displaystyle{\binom{14}{11}(5x)^32^{11}}, as you did, whereas in the second case you

    get \displaystyle{\binom{14}{11}(5x)^{11}2^3} , so what's the correct one?

    In my opinion, they both are, and this perhaps is the reason why the usually ask what the

    coefficient of some power of x is, not what is this or that term.

    Tonio
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