query: Proving a certain sum is 1
positive_passages.docid: 22948
positive_passages.text: Is this binomial coefficient identity known?
negative_passages.docid: 107433
negative_passages.text: Prove the sum to n terms of the series
negative_passages.docid: 153226
negative_passages.text: Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
negative_passages.docid: 79124
negative_passages.text: Proving $\binom {n-1}{r-1}=\sum_{k=0}^r(-1)^k\binom r k \binom{n+r-k-1}{r-k-1}$
negative_passages.docid: 37783
negative_passages.text: Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
negative_passages.docid: 77164
negative_passages.text: If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
negative_passages.docid: 126032
negative_passages.text: Proving a certain inequality
negative_passages.docid: 26741
negative_passages.text: How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
negative_passages.docid: 145274
negative_passages.text: Prove by induction $\sum \frac {1}{2^n} < 1$
negative_passages.docid: 58428
negative_passages.text: Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
negative_passages.docid: 63474
negative_passages.text: Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
negative_passages.docid: 20271
negative_passages.text: Proving $\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$ without induction
negative_passages.docid: 61859
negative_passages.text: Prove $\sum \frac{a}{a+b^4+c^4} \le 1$
negative_passages.docid: 103347
negative_passages.text: combinatorial proof of summation
negative_passages.docid: 108596
negative_passages.text: Proof by induction for "sum-of"
negative_passages.docid: 6539
negative_passages.text: Prove $\sum_{i=1}^n i! \cdot i = (n+1)! - 1$?
negative_passages.docid: 91000
negative_passages.text: Prove that $\frac{1}{a+1}0$