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I'm supposed to use Gauss' law to find the summation of $6k$ from $k=5$ to $n$. Here is my work:

$$6(5)+6(6)+6(7)+⋯+6(n)\\+6(n)+6(n-1)+6(n-2)+...+6(5)$$

When these are added together I get $2S=(30+6n)+(30+6n)+...+(30+6n)$ which is $n(30+6n)$ and then I would divide by $2$, but that gives me $15n+3n^2$ which is incorrect. Where am I going wrong?

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$2S$ is $(n-4)(30+6n)$ instead of $n(30+6n)$ since your $k$ is from $5$ to $n$, so you only have $n-4$ terms.

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