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Results tagged with sequences-and-series
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user 171932
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
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How to prove that these partial binomial sums are zero?
I am trying to prove that the following equation is equal to zero.
$$
0=
\sum_{j=J+1}^N \Big(j (1-q)+ (j-J) (q N-j) \Big) \cdot q^{j} (1-q)^{N -j} \binom{N}{j} \label{zero1}$$
Where
$J,N \in \mat …
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