query: Mathematical Induction: Sum of first n even perfect squares
positive_passages.docid: 16472
positive_passages.text: Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$
negative_passages.docid: 108274
negative_passages.text: Sum of the first $n$ triangular numbers - induction
negative_passages.docid: 138857
negative_passages.text: Proving an inequality by induction, how to figure out intermediate inductive steps?
negative_passages.docid: 153975
negative_passages.text: Proving mathematical induction with arbitrary base using (weak) induction
negative_passages.docid: 91896
negative_passages.text: Induction (Geometric sequence)
negative_passages.docid: 136582
negative_passages.text: Decomposing total sum of squares
negative_passages.docid: 156242
negative_passages.text: As many even numbers as natural numbers.
negative_passages.docid: 40692
negative_passages.text: Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $
negative_passages.docid: 25496
negative_passages.text: Avoiding proof by induction
negative_passages.docid: 6165
negative_passages.text: Proof by Induction $n^2+n$ is even
negative_passages.docid: 20443
negative_passages.text: Calculate sum of squares of first $n$ odd numbers
negative_passages.docid: 42105
negative_passages.text: Fibonacci proof by induction
negative_passages.docid: 72371
negative_passages.text: Proof of Strong Induction Using Well-Ordering Principle
negative_passages.docid: 32950
negative_passages.text: Fake induction proofs
negative_passages.docid: 140841
negative_passages.text: Induction proof of lower bound for $\sum \sqrt n$
negative_passages.docid: 31900
negative_passages.text: Induction on Real Numbers
negative_passages.docid: 107781
negative_passages.text: Detecting perfect squares faster than by extracting square root