Translation of Index Variable of Summation/Examples
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Examples of Translation of Index Variable of Summation
- $\ds \sum_{1 \mathop \le j \mathop \le n} a_j = \sum_{1 \mathop \le j - 1 \mathop \le n} a_{j - 1} = \sum_{2 \mathop \le j \mathop \le n + 1} a_{j - 1}$
Proof
A direct instance of Translation of Index Variable of Summation.
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.3$: Sums and Products: $(6)$