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    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 18th 2014

    Created binomial theorem, and added a relevant lemma to freshman’s dream.

    • CommentRowNumber2.
    • CommentAuthorColin Tan
    • CommentTimeApr 20th 2014

    For the Pascal triangle recurrence to determine the binomial coefficients (nk)\binom{n}{k} where nn and kk are integers, do we also need, for n a positive integer, the boundary condition (nn)=1\binom{n}{n} = 1?

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 20th 2014

    Oh yes, that’s true, we do need another boundary condition to determine (xk)\binom{x}{k}, which can be expressed in any one of various ways, e.g., as (0k)=0\binom{0}{k} = 0 whenever k0k \neq 0. This is for both positive and negative integers kk. Thanks.

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