Proposition: The General Perturbation Method
Let \(n,k\in\mathbb N\) be natural numbers and let \(a_k \in F\) be any elements of a given field \((F, +, \cdot)\).
For a sum \[S_n:=\sum_{0\le k\le n} a_k\] the following property holds:
\[S_n+a_{n+1}=a_0+\sum_{0\le k\le n} a_{k+1}.\]
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References
Bibliography
- Graham L. Ronald, Knuth E. Donald, Patashnik Oren: "Concrete Mathematics", Addison-Wesley, 1994, 2nd Edition
