Some formulas about combinatorics

$$\begin{equation} C_{n+1}^{k+1} = C_n^k + C_n^{k+1} \end{equation}$$ $$\begin{equation} C_k^k + C_{k+1}^k + \cdots + C_n^k = C_{n+1}^{k+1} \end{equation}$$