query: Sum of sum of odd terms of Vandermonde's Identity
positive_passages.docid: 17580
positive_passages.text: Combinatorics That Looks Similar to Vandermonde's Identity
negative_passages.docid: 146746
negative_passages.text: A formula for the sum of the triangular numbers?
negative_passages.docid: 90904
negative_passages.text: Combinatorial proof of an identity with squared binomial coefficients
negative_passages.docid: 65983
negative_passages.text: Combinatorial proof of binomial coefficient summation identity
negative_passages.docid: 86900
negative_passages.text: Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum
negative_passages.docid: 128913
negative_passages.text: A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
negative_passages.docid: 81589
negative_passages.text: Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
negative_passages.docid: 92440
negative_passages.text: Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
negative_passages.docid: 119552
negative_passages.text: Summing Finitely Many Terms of Harmonic Series: $\sum_{k=a}^{b} \frac{1}{k}$
negative_passages.docid: 150822
negative_passages.text: Finding $\sum_{k=0}^{n-1}\frac{\alpha_k}{2-\alpha_k}$, where $\alpha_k$ are the $n$-th roots of unity
negative_passages.docid: 20443
negative_passages.text: Calculate sum of squares of first $n$ odd numbers
negative_passages.docid: 12812
negative_passages.text: Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $
negative_passages.docid: 31970
negative_passages.text: Alternating sum of squares of binomial coefficients
negative_passages.docid: 114414
negative_passages.text: Sum of $\sum_{k=1}^n\sin{k\theta}$
negative_passages.docid: 99453
negative_passages.text: Sum of $k$-th powers
negative_passages.docid: 148883
negative_passages.text: Sum of the series $\frac{1}{2\cdot 4}+\frac{1\cdot3}{2\cdot4\cdot6}+\dots$
negative_passages.docid: 126105
negative_passages.text: Compute $\sum_{k=1}^{n} \frac 1 {k(k + 1)} $