I have the following arithmetic sequence where i need to turn it into a series and evaluate its sum but i have no idea how to derive the series.
$1+2-3+4-5+6-7+...+2000$
I've tried with $(-1)^n.n$ where $n=1$ but it doesn't match the equation.
Really appreciate if you can advice on this.
Evaluate the sum of $1+2-3+4-5+6-7+...+2000$
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sequences-and-series
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3You sure it's not $1-2+3-4+5...+2000$ – 2017-02-12
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4If you can evaluate `-1+2-3+4-5+6-7+…+2000`, simply add `2` to the result to get `1+2-3+4-5+6-7+…+2000`. – 2017-02-12
2 Answers
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Well, I believe you could use that $$1+2+(-3+4)+\dots+(-1999+2000)=1+2+1+\dots+1$$ Note that there are $999$ pairs of $(-3,4), (-5, 6)$ and so on.
So there are $999$ set of $1$s that come after the initial $1,2$. So the answer is $$1+2+1+\dots+1=3+999 \times 1=1002$$
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@S.C.B answer is correct, for the sum of the series. As for your other question, you're concerned that the first term doesn't fit the n*(-1)^n expression that works for all the other terms. I don't think there's a way to make it fit. Your answer for the series part of the question will need to be 1 plus the series for n values 2 through 2000. One of the comments hinted it might be a misprint, or somesuch. It seems that way, but it's not an impediment for calculating the sum.