query: Sequence $x_{n+1} = \sqrt{x_n x_{n-1}}$
positive_passages.docid: 149806
positive_passages.text: Is it possible to utilize the convergence of the sequence $z_{n+1}=a/(1+z_n)$ to prove that the sequence $x_{n+2} = \sqrt{x_{n+1} x_n}$ is convergent?
negative_passages.docid: 49828
negative_passages.text: Show that the sequence $\sqrt{2},\sqrt{2\sqrt{2}},\sqrt{2\sqrt{2\sqrt{2}}},...$ converges and find its limit.
negative_passages.docid: 108429
negative_passages.text: Show that if $x_n \to x$ then $\sqrt{x_n} \to \sqrt{x}$
negative_passages.docid: 130476
negative_passages.text: Prove that every terms of a sequence defined by a recurrence relation is a perfect square.
negative_passages.docid: 34025
negative_passages.text: Limit of the Sequence: $a_{n+1}=a_n+\frac{1}{a_n}$ with $a_1=1$
negative_passages.docid: 151226
negative_passages.text: Why is the sequence $x(n) = \log n$ **not** Cauchy?
negative_passages.docid: 31930
negative_passages.text: Given the sequence $(x_n)$ is unbounded, show that there exist a subsequence $(x_{n_k})$ such that $\lim(1/x_n)=0$.
negative_passages.docid: 47922
negative_passages.text: Prove that the sequence $(a_n)$ defined by $a_0 = 1$, $a_{n+1} = 1 + \frac 1{a_n}$ is convergent in $\mathbb{R}$
negative_passages.docid: 27217
negative_passages.text: For the Fibonacci sequence prove that $\sum_{i=1}^n F_i= F_{n+2} - 1$
negative_passages.docid: 123253
negative_passages.text: Limit of a sequence $a_1=1;a_{n+1}=(n+1)(1+a_n)$
negative_passages.docid: 71639
negative_passages.text: Proof $(1+1/n)^n$ is an increasing sequence
negative_passages.docid: 142
negative_passages.text: Showing the sequence converges to the square root
negative_passages.docid: 104268
negative_passages.text: Confusion on how to solve this question about sequences.
negative_passages.docid: 27756
negative_passages.text: Find a formula for a sequence $\{\sqrt{3},\sqrt{3\sqrt{3}},\sqrt{3\sqrt{3\sqrt{3}}},...\}$
negative_passages.docid: 64885
negative_passages.text: Irrational and rational sequence proof
negative_passages.docid: 91528
negative_passages.text: sequence $x_{n+1}=x_n+e^{-2018x_n}$
negative_passages.docid: 3211
negative_passages.text: The sequence $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}, x_0>0$ is bounded?