Answer
The formula is $n \cdot(n+1)$
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Once again we arrange the terms of our expression $2+4+6+\ldots+2 \cdot n$ into
pairs. The number of pairs in this case is $n .$
$2+2 \cdot n=2 \cdot(n+1)$
$4+(2 \cdot n-2)=2 \cdot(n+1)$
$6+(2 \cdot n-4)=2 \cdot(n+1)$
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2. $n+2=2 \cdot(n+1)$
The total sum $n \cdot 2 \cdot(n+1)$ is twice the sum we are looking for.
Dividing by two will lead us to the final formula $\frac{n \cdot 2 \cdot(n+1)}{2}=n \cdot(n+1)$
Work Step by Step
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