Let \( (a_n)_{n=0}^{\infty} \) be a sequence of real numbers which converge to 0, i.e., \( lim_{n \rightarrow \infty} a_n = 0 \). Then the series \( \sum_{n=0}^{\infty}(a_n - a_{n+1}) \) converges to \( a_0 \).
A post on The Math Forum talks about the naming of this series:
