query: How to find closed form by induction
positive_passages.docid: 26901
positive_passages.text: induction proof: $\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$
negative_passages.docid: 58972
negative_passages.text: Proof/Derivation of Closed form of Binomial Expression $\sum\limits_{k=0}^{2n}(-1)^k\binom{2n}{k}^2$
negative_passages.docid: 101899
negative_passages.text: Proof By Induction of a Sum
negative_passages.docid: 28541
negative_passages.text: How to prove the mathematical induction is true?
negative_passages.docid: 87479
negative_passages.text: Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
negative_passages.docid: 125220
negative_passages.text: Solving binomial theorem via induction
negative_passages.docid: 634
negative_passages.text: Closed form formula for $\sum\limits_{k=1}^n k^k$
negative_passages.docid: 10141
negative_passages.text: Find closed form expression for series expansion coefficients
negative_passages.docid: 51211
negative_passages.text: Mathematics induction (exponential divisible by 2304)
negative_passages.docid: 4991
negative_passages.text: Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
negative_passages.docid: 64437
negative_passages.text: Proof by induction (power rule of the derivative)
negative_passages.docid: 124584
negative_passages.text: How to proof that $\forall n \ge 1: \sum_{i=1}^n (i(i+1))^{-1} = n(n+1)^{-1}$ using mathematical induction
negative_passages.docid: 46698
negative_passages.text: Showing a set is closed under inverses
negative_passages.docid: 135509
negative_passages.text: Proof writing: how to write a clear induction proof?
negative_passages.docid: 39199
negative_passages.text: closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
negative_passages.docid: 10180
negative_passages.text: How to prove that this set is closed?
negative_passages.docid: 12487
negative_passages.text: Prove derangement formula by induction