Answer
\begin{equation}
The\ sum\ is\ 1275
\end{equation}
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By applying the same logic Gauss applied, we notice that for the sum
$2+4+\ldots+100$ we can group the numbers from $2$ to $100$ into $25$ pairs
of the form
$2+100=102$
$4+98=102$
$\cdot$
$\cdot$
$\cdot$
$50+52=102$
The total sum is $25 \cdot 102=2550$
It is easy to notice that 2550 is actually twice the sum we are looking for
which is $2550 / 2=1275$
So $2+4+\ldots+100=1275$
Work Step by Step
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