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For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.

2 votes
5 answers
940 views

Binomial series

I am interested in the limit $\frac{\sum_{k=0}^n \sqrt{k}\cdot\binom{n}{k}}{\sqrt{n}\cdot2^n}$ as $n$ goes to infinity. Any reference or argument? In general what do we know about the asymptotic behav …