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Results tagged with sequences-and-series
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user 265714
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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Closed form of $ \sum_{k_{j-1}=0}^{k_j}....\sum_{k_1=0}^{k_2} \sum_{k=0}^{k_1} k^m $ as a po...
Consider how the iterated sum $ \sum_{k_{j-1}=0}^{k_j}....\sum_{k_1=0}^{k_2} \sum_{k=0}^{k_1} 1 $ produces the diagonals on pascal's triangle, so it has a nice closed form. Does the iterated sum $ \su …
- 1,109
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Is there a closed form of $\sum_{i=1}^{n-k} {n-1-i\choose k-1}x^i$ in $x$?
I'm looking for the generating function of the sum $\sum_{i=1}^{n-k} {n-1-i\choose k-1}x^i$. One can compute this using the Euler-MacLauren formula but the remainder term is a little messy. Is there …
- 1,109