The whole series can be rewritten as: +x^0- x^1+ x^2- x^3+...(-x)^n The lower limit would be i=0; if it was i=1 (or any other odd number for that matter), then the degrees of the x-terms (x, x^2, x^3...) would be correct, but the first term (-x^1) would be negative, and the rest of their signs would also be flipped. If we start at zero, then the first term is positive and is 1; the second term is negative, and is of degree one; the third, positive degree-two etc. The rule is, then, (-1^i)(x^i), which can be rewritten as (-x^i). The series seems to end at (-x)^n for whatever n, so the upper limit must be n. However, if the series didn't end at n and kept going (denoted with an ellipsis after (-1^n)(x^n)), then the upper limit would be infinity. Finally, the whole thing must look [url=http://gyazo.com/ab9926d467fbef63804bf32024c7f208]like this.[/url] Good luck.