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$\large a_{n}=\sum_{k=1}^{n}\frac{k}{2^k}$ 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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