query: Limit of Sequence $x_n = (x_{n-1} +x_{n-2})/2$
positive_passages.docid: 46685
positive_passages.text: Show that the sequence $a_1=1$, $a_2=2$, $a_{n+2} = (a_{n+1}+a_n)/2$ converges by showing it is Cauchy
negative_passages.docid: 20136
negative_passages.text: Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $
negative_passages.docid: 155695
negative_passages.text: The convergence of a sequence
negative_passages.docid: 67420
negative_passages.text: Limit of quotient sequence
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?
negative_passages.docid: 29266
negative_passages.text: Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$
negative_passages.docid: 19898
negative_passages.text: Limit $\lim (1+(a^{1/n}-1) / b)^n$
negative_passages.docid: 67638
negative_passages.text: Show that $x_{n+1}=x_n(2-ax_n)$ converges and find the limit
negative_passages.docid: 107764
negative_passages.text: Limit series $(a^n-b^n)^{1/n}$
negative_passages.docid: 144786
negative_passages.text: Show that the following inductively defined sequence converges and find its limit.
negative_passages.docid: 74629
negative_passages.text: Find the limit of the sequence $\{\frac{x_1 + 2x_2 + ... + nx_n}{n^2}\}$, where $\{x_n\}$ is a convergent sequence in a normed space S.
negative_passages.docid: 158960
negative_passages.text: How to find limit of the sequence $\sum\limits_{k=1}^n\frac{1}{\sqrt {n^2 +kn}}$?
negative_passages.docid: 50673
negative_passages.text: Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$
negative_passages.docid: 142509
negative_passages.text: If $\alpha\in (0,1]$ and $x_n=\alpha x_{n-1}+(1-\alpha)x_{n-2}$, show that the sequence $\{x_n\}$ is convergent.
negative_passages.docid: 148492
negative_passages.text: Finding the limit of the sequence $(1 - 1/\sqrt 2) \dotsm ( 1 - 1/\sqrt {n+1})$
negative_passages.docid: 80440
negative_passages.text: Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
negative_passages.docid: 108929
negative_passages.text: Proving the limit of a function of a sequence is equal to the function of the limit of that sequence