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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Lower/Upper bounds for $ \sum\limits_{i=0}^k \binom ni x^i $
Are there good lower/upper bounds for
$ \sum\limits_{i = 0}^k {\left( \begin{array}{l} n \\ i \\ \end{array} \right)x^i } $ where $0<x<1$, $k \ll n$?