Medium Practice — Set 2

Quick Recap — Coefficient Identities

• $\sum_r{}^nC_r=2^n$; $\sum_r(-1)^r{}^nC_r=0$.
• Sum of even-indexed $=$ sum of odd-indexed $=2^{n-1}$.
• $\sum_r{}^nC_r^{\,2}={}^{2n}C_n$; the coefficient of $x^n$ in $(1+x)^{2n}$ is $^{2n}C_n$.
• Sum of coefficients of a polynomial $p(x)$ is $p(1)$.