Simple High school Series & Limits

Calculus Level 4

an=k=1nk2k\large a_{n}=\sum_{k=1}^{n}\frac{k}{2^k} Suppose we define the sequence ana_n as above with natural number (n), find the value of

limn2n(63an)n2+5n+1\lim_{n\rightarrow \infty }\frac{2^n(6-3a_{n})}{\sqrt{n^2+5n+1}}

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