query: Recurrence relation $x_{n+1}=x_n-x_{n}^2$ with $x_1=1/2$
positive_passages.docid: 144165
positive_passages.text: $n\in N, a_{n+1} = a_n (1 - a_n)$ , $0 < a_0 < 1$. Prove that $\lim\limits_{n\to\infty} a_n\cdot n = 1$.
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: 60747
negative_passages.text: Recurrence relation using substitution method
negative_passages.docid: 85217
negative_passages.text: Boundedness and convergence of $x_{n+1} = x_n ^2-x_n +1$
negative_passages.docid: 50444
negative_passages.text: Laguerre polynomials recurrence relation
negative_passages.docid: 13418
negative_passages.text: Solve the recurrence
negative_passages.docid: 78472
negative_passages.text: Sequence is periodic $x_{n+2}=|x_{n+1}-x_{n-1}|$
negative_passages.docid: 43327
negative_passages.text: convoluted recurrence: $f(2n)=f(n)+f(n+1)+n, f(2n+1)=f(n)+f(n-1)+1$
negative_passages.docid: 89705
negative_passages.text: How to solve $a_n = 2a_{n-1} + 1, a_0 = 0, a_1 = 1$?
negative_passages.docid: 21137
negative_passages.text: Recurrence relation, induction and Fibonacci numbers
negative_passages.docid: 100232
negative_passages.text: Find equivalent of recurrent sequence $u_1=1$, $u_{n+1}=1+\frac n {u_n}$
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: 17492
negative_passages.text: Recurrence telescoping $T(n) = T(n-1) + 1/n$ and $T(n) = T(n-1) + \log n$
negative_passages.docid: 123253
negative_passages.text: Limit of a sequence $a_1=1;a_{n+1}=(n+1)(1+a_n)$
negative_passages.docid: 83784
negative_passages.text: Fixed Point of $x_{n+1}=i^{x_n}$
negative_passages.docid: 151929
negative_passages.text: Solving recurrence relation. Recurrence
negative_passages.docid: 39739
negative_passages.text: Fibonacci identity: $f_{n+1}f_{n-1} = f_n^2 + (-1)^n$