Question:
Write the sum of the series 2 + 4 + 6 + 8 + ... + 2n.
Solution:
$S_{n}=2+4+6+8+\ldots+2 n$
$=\frac{n}{2}[4+(n-1) 2]$
$=\frac{n}{2}[2+2 n]$
$=n[n+1]$
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