query: Simplification of a special iterated sum
positive_passages.docid: 150092
positive_passages.text: Iterated sums and asymptotics
negative_passages.docid: 124229
negative_passages.text: Simplify $\sum_{k=0}^{\infty} x^ky^{\frac{k(k+1)}{2}}$
negative_passages.docid: 55061
negative_passages.text: Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $
negative_passages.docid: 145322
negative_passages.text: Sum of a Hyper-geometric series. (NBHM 2011)
negative_passages.docid: 8806
negative_passages.text: Summation of binomial coefficients
negative_passages.docid: 28109
negative_passages.text: Conjectural closed-form representations of sums, products or integrals
negative_passages.docid: 66380
negative_passages.text: Alternating harmonic sum $\sum_{k\geq 1}\frac{(-1)^k}{k^3}H_k$
negative_passages.docid: 133905
negative_passages.text: Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
negative_passages.docid: 3798
negative_passages.text: Finding formula for sum $S_n = \sum_{i=1}^n i(i-1)$
negative_passages.docid: 101017
negative_passages.text: What is the sum of $\sum\limits_{i=1}^{n}ip^i$?
negative_passages.docid: 33104
negative_passages.text: Combinatorial Proof with Summation Identity
negative_passages.docid: 39659
negative_passages.text: Is there a closed formula for this summation?
negative_passages.docid: 55777
negative_passages.text: A tricky sum to infinity
negative_passages.docid: 155479
negative_passages.text: Summation of inner products
negative_passages.docid: 20471
negative_passages.text: Evaluating a slow sum
negative_passages.docid: 482
negative_passages.text: Express $1 + \frac {1}{2} \binom{n}{1} + \frac {1}{3} \binom{n}{2} + \dotsb + \frac{1}{n + 1}\binom{n}{n}$ in a simplifed form
negative_passages.docid: 14197
negative_passages.text: show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$