Telescoping identity.
For any sequence $(Y_n)$,
\(Y_n - Y_0 = \sum_{k=1}^n (Y_k - Y_{k-1}), \qquad n \ge 0.\)
In particular, if $Y_n := \sum_{k=1}^n \Delta Y_k$, then $Y_0 = 0$ by the empty-sum convention.
Telescoping identity.
For any sequence $(Y_n)$,
\(Y_n - Y_0 = \sum_{k=1}^n (Y_k - Y_{k-1}), \qquad n \ge 0.\)
In particular, if $Y_n := \sum_{k=1}^n \Delta Y_k$, then $Y_0 = 0$ by the empty-sum convention.
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