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Good afternoon,

I would like to ask, if anyone knows how to evaluate a sum

$$\sum_{k=0}^{\lambda n}{n \choose k}$$

for fixed $\lambda < 1/2$ with absolute error $O(n^{-1})$, or better.

In Concrete Mathematics (Graham, Knuth, Patashnik), it is shown how to evaluate this sum with absolute error $O(1)$, but it is not clear to me, how to obtain better absolute error in a straightforward manner.

Thank you in advance.

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