Help: sum of binomial coefficents

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    Binomial Sum
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SUMMARY

The discussion centers on deriving a closed formula for the sum of the first s binomial coefficients, represented as \(\sum_{k=0}^{s} \binom{n}{k}\) where \(s < n\). It is concluded that this sum does not have a closed form, as noted by the user Thealchemist83 and confirmed by Istvan. For further reading, the fifth chapter of "Concrete Mathematics" by Graham, Knuth, and Patashnik is recommended for deeper insights into the topic.

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thealchemist83
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Help: sum of binomial coefficents !

Hello!
I cannot figure out how to derive a closed formula for the sum of "the first s" binomial coefficients:

\sum_{k=0}^{s} \left({{n}\atop{k}}\right)

with s&lt;n

Could you please help me find out some trick to derive the formula... I've an exam on monday!

Thank you very much!
 
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Oh nevermind, I misread it as the sum of n binomial coefficients.
 
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Dear Thealchemist83,

I have just read your question, long after your exam... If this was your task, I wonder about the mark you've got because this sum does not have a closed form.:smile:

See the fifth chapter of Concrete Mathematics (Graham, Knuth, Patashnik)

Istvan
 

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