TeX source:

\begin{align*} c_i &= (a_1 + a_2 + ... + a_i) + (a_{i+1} + ... + a_{n+1}) \\ &= (a_1 + a_2 + ... + a_i) + ((a_{i+1} + ... + a_j) + (a_{j+1} + ... + a_{n+1})) \\ &= ((a_1 + a_2 + ... + a_i) + (a_{i+1} + ... + a_j)) + (a_{j+1} + ... + a_{n+1}) \\ &= ((a_1 + a_2 + ... + a_j)) + (a_{j+1} + ... + a_{n+1}) \\ &= c_j \square \end{align*}