TITLE: Moving index in a summation - how does that work?
QUESTION [6 upvotes]: In a book I have they solve an equation like this:
$$\sum_{i=2}^{19} i(i - 2) = \sum_{i=2 - 1}^{19 - 1} (i + 1)(i + 1 - 2) = \sum_{i=1}^{18} (i + 1)(i - 1) = \cdots$$
What I don't get is how it works. If I do $-1$ on the summation index, why do I have to add $+1$ to the variable $i$ used in the terms? Is there a name for this technique and the rules associated with it?

REPLY [5 votes]: If you adjust your clock such that the time it shows is one hour earlier than the actual time (e.g. showing $1$ o'clock when it is actually $2$ o'clock), then you can arrive your appointment one hour later according to the adjusted clock, and still be on time.