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This "+7" would be weird; I can't see the pattern.
For $\displaystyle S=1-3+5-7+\cdots+1001$, there is an easy way: group the terms 2 by 2, you get $\displaystyle S=(1-3)+(5-7)+(9-11)+\cdots+(997-999)+1001$. As you can see, all the parentheses equal -2, and there are ?? of them, so...