query: Form or asymptotic behaviour of $T(n) =2T(n-1)+n$
positive_passages.docid: 79071
positive_passages.text: Solve the recurrence $T(n) = 2T(n-1) + n$
negative_passages.docid: 69791
negative_passages.text: How to solve: T(n) = T(n - 1) + n
negative_passages.docid: 157917
negative_passages.text: Calculate the leading order asymptotic behaviour (with two maxima)
negative_passages.docid: 14487
negative_passages.text: Does $\sum_{n=2}^\infty (n\ln n)^{-1}$ diverge?
negative_passages.docid: 97720
negative_passages.text: Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
negative_passages.docid: 33965
negative_passages.text: Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$
negative_passages.docid: 80440
negative_passages.text: Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
negative_passages.docid: 95862
negative_passages.text: Prove that $t_{n-1, \alpha/2}$ is strictly decreasing in $n$
negative_passages.docid: 122024
negative_passages.text: Asymptotic of a sum involving binomial coefficients
negative_passages.docid: 87479
negative_passages.text: Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
negative_passages.docid: 113016
negative_passages.text: Remainder form of Taylor polynomial at $x_0$: $ \frac{1}{n!}f^{(n)}(x_0 +\theta(x-x_0))(x-x_0)^n$ with $\theta \to \frac{1}{n+1}$ as $ x \to x_0$
negative_passages.docid: 154508
negative_passages.text: The energy method for $u_{tt}-du_t-u_{xx}=0, (0,1)\times(0,T) $
negative_passages.docid: 50087
negative_passages.text: Convergence of $a_{n+1}=\frac{1}{1+a_n}$
negative_passages.docid: 44841
negative_passages.text: Complexity of $T(n) = 2T(n/2) + n$
negative_passages.docid: 127267
negative_passages.text: Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$
negative_passages.docid: 67926
negative_passages.text: $S_n$ is generated by elements of the form $(1k)$
negative_passages.docid: 53005
negative_passages.text: Properties of $\liminf$ and $\limsup$ of sum of sequences: $\limsup s_n + \liminf t_n \leq \limsup (s_n + t_n) \leq \limsup s_n + \limsup t_n$