query: Convergence of a sequence and some of its subsequences
positive_passages.docid: 123609
positive_passages.text: If $\{x_{2m}\}$ and $\{x_{2m-1}\}$ converge to the same limit, does $\{x_m\}$ converge?
negative_passages.docid: 88441
negative_passages.text: Whether the sequence $\{x_n-y_n\}$ converge or not.
negative_passages.docid: 34723
negative_passages.text: Proof of a limit for a recursively-defined sequence
negative_passages.docid: 62937
negative_passages.text: Test for the convergence of the sequence $S_n =\frac1n \left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$
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: 65592
negative_passages.text: Convergence of $a_n=(1/2)^{(1/3)^{...^{(1/n)}}}$
negative_passages.docid: 99934
negative_passages.text: convergence of a sequence based on comparison test
negative_passages.docid: 140424
negative_passages.text: Proof of Divergence for a Sequence
negative_passages.docid: 64721
negative_passages.text: A Sequence converges to a limit $L \in \mathbb R$ if, and only if, an $N$-th tail of the sequences converges to $L$ for some $N \in \mathbb N$
negative_passages.docid: 157179
negative_passages.text: Cesaro Mean of Sequences - Convergence
negative_passages.docid: 17779
negative_passages.text: Proving the Limit of a Sequence of without the Dominated Convergence Theorem
negative_passages.docid: 153736
negative_passages.text: Question about convergence of a simple recursive sequence
negative_passages.docid: 107399
negative_passages.text: A sequence and convergence
negative_passages.docid: 20136
negative_passages.text: Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $
negative_passages.docid: 107735
negative_passages.text: What does the following sequence converge to?
negative_passages.docid: 74542
negative_passages.text: Convergence of a sequence whose even and odd subsequences converge
negative_passages.docid: 55464
negative_passages.text: Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$