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Thread: Binomial Question

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    Binomial Question

    Use (1+x)^n=(1+x)(1+x)^n-1 to prove that nCk= n-1Ck + n-1Ck-1

    Thanks.
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    Re: Binomial Question

    Try expand and equate coefficients of x^k on both sides (which is seen by the nCk on the LHS.

    I'll write a solution later if needed
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    Re: Binomial Question

    Quote Originally Posted by pikachu975 View Post
    Try expand and equate coefficients of x^k on both sides (which is seen by the nCk on the LHS.

    I'll write a solution later if needed
    I understand what you mean, but i'm unsure on how to get the coeff of x^k on the RHS.

    Thanks.
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    Re: Binomial Question

    Quote Originally Posted by Andy005 View Post
    I understand what you mean, but i'm unsure on how to get the coeff of x^k on the RHS.

    Thanks.
    You can see you have a (1+x) so for the (1+x)^(n-1) you need an x^(k-1) and an x^k because if you expand (1+x)(1+x)^(n-1) you can see the 1 will multiply with the term with x^k and the x will multiply with the term x^(k-1) to give x^k.
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    Re: Binomial Question

    Quote Originally Posted by pikachu975 View Post
    You can see you have a (1+x) so for the (1+x)^(n-1) you need an x^(k-1) and an x^k because if you expand (1+x)(1+x)^(n-1) you can see the 1 will multiply with the term with x^k and the x will multiply with the term x^(k-1) to give x^k.
    So if i were to expand (1+x)^n-1 would it be,

    n-1C0 + n-1C1x + n-1C2x^2 + ... + n-1Ck-1x^k-1 + n-1Ckx^k + ... + n-1Cn-1x^n-1?
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    Re: Binomial Question

    Quote Originally Posted by Andy005 View Post
    So if i were to expand (1+x)^n-1 would it be,

    n-1C0 + n-1C1x + n-1C2x^2 + ... + n-1Ck-1x^k-1 + n-1Ckx^k + ... + n-1Cn-1x^n-1?
    Yep that's right
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    Re: Binomial Question

    Quote Originally Posted by pikachu975 View Post
    Yep that's right
    Thanks for your help.
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