In the binomial expansion of (1 + a)m + n, prove that the coefficient of am and an are equal.
We have (1 + a)m + n = [m + nC₀ + m + nC₁a + m + nC₂a² + ... + m + nCₙaⁿ + ... + m + nCₘam]
Coefficient of am = m + nCₘ = (m + n)! / (m! n!)
Coefficient of an = m + nCₙ = (m + n)! / (m! n!)
Clearly, m + nCₘ = m + nCₙ
Hence proved: The coefficients of am and an are equal.