Cho n thuộc N*. Chứng minh C 0 n + C 1 n + C 2 n + + C (n -1) n + C n n = 2^n

* Hướng dẫn giải

Ta có:

$$\begin{gathered} {\left(x+1\right)}^n=C_n^0{x}^n+C_n^1{x}^{n-1}.1+C_n^2{x}^{n-2}.1^2+\mathrm{...}+C_n^{n-1}x.1^{n-1}+C_n^n.1^n \\ =C_n^0{x}^n+C_n^1{x}^{n-1}+C_n^2{x}^{n-2}+\mathrm{...}+C_n^{n-1}x+C_n^n. \end{gathered}$$