First difference
= First difference
{title2=$\Delta u_n=u_{n+1}-u_n$}
The first difference of a <sequence> records the change between consecutive terms. Its partial sums telescope: $u_n=u_0+\sum_{j=0}^{n-1}\Delta u_j$. Thus a compact description of the differences can give an efficient way to reconstruct distant terms of the original <sequence>.