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For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.
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Estimation of a combinatorial sum when $n$ is large
Suppose $c,t$ are such that, $0< c< 1$ constant and $cn\leq t \leq n$.
I want to have an estimation of
$\sum _{i=0}^{cn} {cn\choose {i}}{(1-c)n \choose t-i} 2^{t-i}$
when n goes to infinity.
Can I …