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.
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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}]} & @@@
Thread[{Range[2^(n - 1)],
Riffle[sq, #] & /@ s, (({1}~Join~#).ReleaseHold[sq] & /@ t)}],
Frame -> All, BaseStyle -> {FontFamily -> "Kartika", Blue, 12}]]
for example:f[3]
or f[5]
If the sign of first term is also included then $2^n$ and code can be simplified.
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$\begingroup$ You beat me to it, and with a solution that's more elegant than what I was working on, both from the code and from the presentation perspective, so I don't even feel bad about it ;-) (+1) $\endgroup$– MarcoBCommented May 13, 2015 at 10:00
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$\begingroup$ @MarcoB thank you for kind words and vote...variety of answers makes this site so enjoyable and instructive :) $\endgroup$– ubpdqnCommented May 13, 2015 at 10:03