Pascal's addition rule

C(n,k) = C(n-1,k-1) + C(n-1,k), eq (1.28). Eq (1.60) proves it by writing the right-hand terms as (n-1)!/((k-1)!(n-k)!) and (n-1)!/(k!(n-k-1)!), whose common-denominator sum is n!/(k!(n-k)!).

Usage

PascalId(n, k)

Arguments

n, k

requires 1 <= k <= n - 1.

Value

list(n, k, lhs, rhs, term_left, term_right, forms_agree).

References

Morin, D. J. (2016). Probability: For the Enthusiastic Beginner. Createspace. Eqs. (1.28), (1.60).

Examples

PascalId(5, 2)$lhs
#> [1] 10