Question

In the expansion $(1+a{)}^{m+n}$, prove that coefficients of $a^m$ and $a^n$ are equal

Answer 1

coeff of $A^m{=}^{m+m}{C}_m=\frac{\angle m+n}{\angle m\angle m}...\left(1\right)$

coeff of $a^n{=}^{m+n}{C}_n=\frac{\angle m+n}{\angle n\angle m}...\left(2\right)$

$\therefore$ coeff of $a^m=$ coeff of $a^n$