[xg15]

True. I feel, this is why sometimes, the notation

  a_0 + a_1 + ... + a_n

is easier to understand than the shorter

  sum(i = 0 to n) a_i

.

But on the other hand, 2 or 3 elements of the sum are usually enough, i.e. you probably wouldn't improve understanding by writing out the first 10 elements or so.

[gowld]

Neither of those forms is sufficient information to solve a problem, except for a "guess what I'm thinking" puzzle.

You need:

   sum(i = 0 to n) *f*(i)

and you'd like:

   Example: f(0) = *a_0*, f(1) = *a_1*, f(2) = *a_2*

where the stuff in *italics* is given as a concrete substitution.