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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 $\binom{n}{k}$ where $n$ and $k$ are integers, do we also need, for n a positive integer, the boundary condition $\binom{n}{n} = 1$?

• CommentRowNumber3.
• CommentAuthorTodd_Trimble
• CommentTimeApr 20th 2014

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