query: Prove sequence $H_n=1+\frac{1}{2}+\frac{1} {3}+\dots+\frac{1}{n}$ does not converge.
positive_passages.docid: 14031
positive_passages.text: Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?
negative_passages.docid: 49507
negative_passages.text: Is this sequence convergent?
negative_passages.docid: 17201
negative_passages.text: $y_{2n}, y_{2n+1}$ and $y_{3n}$ all converge. What can we say about the sequence $ y_n$?
negative_passages.docid: 35885
negative_passages.text: Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
negative_passages.docid: 79266
negative_passages.text: Proving a sequence defined by a recurrence relation converges
negative_passages.docid: 48500
negative_passages.text: Proof of convergence of sequences
negative_passages.docid: 99542
negative_passages.text: Does the series $1 + \frac{1}{2} - \frac{1}{3} + \frac{1}{4} + \frac{1}{5} - \frac{1}{6} + \dots$ converge?
negative_passages.docid: 60217
negative_passages.text: Proof: Series converges $\implies $ the limit of the sequence is zero
negative_passages.docid: 90936
negative_passages.text: how prove $\sum_{n=1}^\infty\frac{a_n}{b_n+a_n} $is convergent?
negative_passages.docid: 99933
negative_passages.text: Determine whether $(x_n)$ converges if $x_1= a , x_{n+1} = x_n+\frac{1}{x_n}$ for $n \in \mathbb{N}$
negative_passages.docid: 111353
negative_passages.text: Show that $\{a_n\}$ defined by $a_{n+1}=\frac{a_n+2}{a_n+1}$ converges
negative_passages.docid: 25674
negative_passages.text: Bounded sequence which is not convergent, but differences of consecutive terms converge to zero
negative_passages.docid: 19657
negative_passages.text: Does the recursive sequence $a_1 = 1, a_n = a_{n-1}+\frac{1}{a_{n-1}}$ converge?
negative_passages.docid: 104344
negative_passages.text: Prove if $|a_{n+1}|/|a_n| \leq |b_{n+1}|/|{b_n}|$ and $\sum |b_n|$ is convergent, then $\sum |a_n|$ is convergent
negative_passages.docid: 60405
negative_passages.text: Showing a recursive sequence isn't bounded $a_{n+1}=a_n+\frac 1 {a_n}$
negative_passages.docid: 12480
negative_passages.text: Convergence of $\sum_{n=1}^{\infty} \frac{\frac{1}{2}+(-1)^n}{n}$
negative_passages.docid: 93545
negative_passages.text: Showing the sequence converges $a_{1}=\frac{1}{2}$, $a_{n+1}=\frac{1}{2+a_{n}}$