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Results tagged with binomial-coefficients
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user 33767
For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.
3
votes
0
answers
401
views
Weighted sum of ratio of partial sum of binomial coefficients
I would like to approximate the following sum when $n \rightarrow \infty$ and $n \gg k$,
$\sum_{x = k}^n \sum_{y > x}^n \frac{\sum_{m = 0}^{k - 1} {y - 2 \choose m}}{\sum_{m = 0}^k {y - 1 \choose m}} …
- 83
5
votes
1
answer
679
views
Summing ratio of ratio of partial sums of binomial coefficients
I would like to approximate the following when $n \gg k$.
$\sum_{y = k + 1}^n \frac{\sum_{m = 0}^{k - 1} {y - 2 \choose m} (y - 1)}{\sum_{m = 0}^k {y - 1 \choose m}}.$
The formula can be re-written …
- 83