# series combinations

is there any possibility of displaying all possible series of the form: "1+/-2^2+/-3^2+/-...+/-n^2", where one can choose the sign before the each term and knows the numbers of the terms in the series? (Summing up I would like to find out all possible combinations of the signs.) I appreciate your help.

For n terms there are $2^{n-1}$ arrangements of signs of terms after first term. If the aim (for small n) is to display some examples of all sign arrangements for n-1 terms after first term then here is a way. There are doubtless much better ways.

f[n_?Positive] :=
With[{t = Tuples[{-1, 1}, n - 1], s = Tuples[{"-", "+"}, n - 1],
sq = HoldForm[#^2] & /@ Range[1, n]},
Grid[{#1, Row[{Row@#2, " = ", #3}]} & @@@

for example:f[3]
or f[5]
If the sign of first term is also included then $2^n$ and code can be simplified.