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According to Wikipedia: Pascal's rule, C(n,k)+C(n,k-1)=C(n+1,k) applies when 0<k<=n+1. But this page says it only applies when 0<k<n. Wikipedia's proof of this version of Pascal's rule involves multiplication by k/k, and by (n+1-k)/(n+1-k). What, if anything, prevents k=n?

Reading on, Corwin seems to only take care to avoid the case where k is strictly greater than n: "In our sum, this means we need to split out the k=0 and k=n+1 terms before applying Pascal's identity." (I've standardised his labelling of variables in this quote.)

Reading on, Corwin seems to only take care to avoid the case where k is strictly greater than n: "In our sum, this means we need to split out the k=0 and k=n+1 terms before applying Pascal's identity." (I've standardised his labelling of variables in this quote.)

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