query: Using induction to study the sequence $\sqrt{6} , \sqrt{6 +\sqrt{6}}, \dots$
positive_passages.docid: 686
positive_passages.text: $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
negative_passages.docid: 101899
negative_passages.text: Proof By Induction of a Sum
negative_passages.docid: 42105
negative_passages.text: Fibonacci proof by induction
negative_passages.docid: 130093
negative_passages.text: Prove by Induction : $n < 2^n$
negative_passages.docid: 76696
negative_passages.text: Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
negative_passages.docid: 158404
negative_passages.text: Sequence generated by arithmetic and harmonic mean converges to square root
negative_passages.docid: 145255
negative_passages.text: Fibonacci, tribonacci and other similar sequences
negative_passages.docid: 94601
negative_passages.text: Mathematical Induction Question About A Basis Step
negative_passages.docid: 123757
negative_passages.text: Proving a summation inequality with induction
negative_passages.docid: 67886
negative_passages.text: How to prove $\sum_{k=1}^{n}F_k = F_{n+2}-1$ by induction when $F_n$ is the Fibonacci sequence
negative_passages.docid: 150647
negative_passages.text: How many $6$-lentgh increasing sequence are there from $1$ to $49$?
negative_passages.docid: 157601
negative_passages.text: Proof a formula of the Fibonacci sequence with induction
negative_passages.docid: 107810
negative_passages.text: Induction with Binomial Coefficients
negative_passages.docid: 42285
negative_passages.text: Prove by mathematical induction.
negative_passages.docid: 142
negative_passages.text: Showing the sequence converges to the square root
negative_passages.docid: 124917
negative_passages.text: Fibonacci numbers and proof by induction
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) $