query: Find the $n$th term of sequence in the form of $a_{n+2}=ba_{n+1}+ca_n+d$
positive_passages.docid: 83346
positive_passages.text: Finding a closed form $x_n$ for the recurrence relation $x_{n+2} = px_{n+1} + qx_n + r$
negative_passages.docid: 107098
negative_passages.text: Find an explicit formula for the recurrence $a_n = n(a_{n-1} + a_{n-2})$ knowing that $ a_0=1$ and $a_1=2$.
negative_passages.docid: 70561
negative_passages.text: limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$
negative_passages.docid: 13789
negative_passages.text: solve $T(n)=T(n-1)+T(\frac{n}{2})+n$
negative_passages.docid: 55464
negative_passages.text: Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$
negative_passages.docid: 69791
negative_passages.text: How to solve: T(n) = T(n - 1) + n
negative_passages.docid: 50087
negative_passages.text: Convergence of $a_{n+1}=\frac{1}{1+a_n}$
negative_passages.docid: 86205
negative_passages.text: Evaluating the limit of a sequence given by recurrence relation $a_1=\sqrt2$, $a_{n+1}=\sqrt{2+a_n}$. Is my solution correct?
negative_passages.docid: 75279
negative_passages.text: Reversing the $T(n) = \frac{n(n+1)}{2}$ formula
negative_passages.docid: 70460
negative_passages.text: How can I solve the following sequence
negative_passages.docid: 132358
negative_passages.text: Is the sequence $a_{n+1}=a_n-\frac{1}{a_n}$, $a_0=2$ bounded?
negative_passages.docid: 78472
negative_passages.text: Sequence is periodic $x_{n+2}=|x_{n+1}-x_{n-1}|$
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: 686
negative_passages.text: $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
negative_passages.docid: 145863
negative_passages.text: sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges
negative_passages.docid: 144260
negative_passages.text: Solve recurrence relation $a_n = 3 a_{n - 3} + a_{n-1} + 2 n$
negative_passages.docid: 74522
negative_passages.text: Convergence of a sequence, $a_n=\sum_1^nn/(n^2+k)$