query: Does this sequence converge to L?
positive_passages.docid: 71798
positive_passages.text: $\lim_{n\to \infty}\frac{1}{n} \sum_{k=1}^n x_k =x\;$ given $\;\lim_{n\to \infty} x_n= x\;?$
negative_passages.docid: 110568
negative_passages.text: Does $\sum_{k=1}^{\infty}\ln(\frac{k}{k+1})$ converge/diverges??
negative_passages.docid: 100580
negative_passages.text: Proof that a sequence converges.
negative_passages.docid: 123609
negative_passages.text: If $\{x_{2m}\}$ and $\{x_{2m-1}\}$ converge to the same limit, does $\{x_m\}$ converge?
negative_passages.docid: 73906
negative_passages.text: Prove that subsequence converges to limsup
negative_passages.docid: 113585
negative_passages.text: Does $\sum\limits_{k=1}^∞\frac1{k^{\ln k}}$ converge or diverge?
negative_passages.docid: 49419
negative_passages.text: Does $a_n$ converges if and only if $a_{2n},a_{3n},a_{2n-1}$ converge?
negative_passages.docid: 94409
negative_passages.text: showing that the sequence $a_n=1+\frac{1}{2}+...+\frac{1}{n} - \log(n)$ converges
negative_passages.docid: 64081
negative_passages.text: Sequence converging to different limits
negative_passages.docid: 138052
negative_passages.text: How to work out the limit of  this bounded sequence?
negative_passages.docid: 143642
negative_passages.text: Does the sequence $(\sqrt{n} \cdot 1_{[0, 1/n]})_n$ converge weakly in $L^2$?
negative_passages.docid: 34677
negative_passages.text: Sequence Converging to Supremum
negative_passages.docid: 155695
negative_passages.text: The convergence of a sequence
negative_passages.docid: 88365
negative_passages.text: Prove the sequence converge and find its limit
negative_passages.docid: 147849
negative_passages.text: Does $(n!)/n^{1000}$ diverge or converge
negative_passages.docid: 18219
negative_passages.text: (ZF)subsequence convergent to a limit point of a sequence
negative_passages.docid: 69989
negative_passages.text: Do the following series converge if $a_n>0$ and $ \sum_{n=1}^{\infty}a_n$ diverges?