# Use the approach in Gauss's Problem to find the following

Use the approach in Gausss
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Consider the series $1+2+3+4+\dots +1001$.
For the series $1+2+3+4+\dots +1001$, it is clear that there are $1001$ terms, which is odd.
So, add the series to itself in reverse order.
Note that each pair has a sum of $1002$ and there are $1001$ pairs which gives:
$1002\left(1001\right)=1003002$
Since this is the sum of the series added to itself, the sum of the original series is half this sum.
The sum of $1+2+3+4+\dots +1001$ is then $\frac{1}{2}\left(1003002\right)=501501$