Rewriting summation formula I just watched a tutorial on recurrence by substitution. In the tutorial, it mentioned about rewriting
$\sum\limits_{i=1}^\mathbb{k}{2^i}$
as (2k+1 - 2). My question is can I generalize it as xlimit + 1 - x where x is the base. 

Nice observation and almost true:
$$
\sum\limits_{i=1}^\mathbb{n}{a^i} = \frac{a^{n+1}-a}{a-1}
$$
It's a special case of a geometric progression.
