\[\large a_{n}=\sum_{k=1}^{n}\frac{k}{2^k}\] Suppose we define the sequence \(a_n\) as above with natural number (n), find the value of

\[\lim_{n\rightarrow \infty }\frac{2^n(6-3a_{n})}{\sqrt{n^2+5n+1}}\]

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