Question

Using mathematical induction, prove that

^mC₀ ⁿC_k + ^mC₁ ⁿC_{k - 1} + ....+ ^mC_k ⁿC₀ = ^{m + n}C_k 

where m, n, k are positive integers, and ^pC_q = 0 for p < q.

Answer 1

Thus, P (1, 1) is true.

Now, let us assume that P (m, n) holds for any fixed value of m and n. ie,

Hence, P (m + 1, n + 1) is true.