Recursion formula for: $a_n = \left(\frac12\right)^n+2n−1$
58088
Find recursive formula for sequence $a_n = \left(\frac23\right)^n + n$
155353
Find the limit of $ a_n =\left(1+\frac{1^2}{n^2}\right)^1\left(1+\frac{2^2}{n^2}\right)^2\cdots \left(1+\frac{n^2}{n^2}\right)^n$
68853
Is there any formula for the series $1 + \frac12 + \frac13 + \cdots + \frac 1 n = ?$
35169
Finding the limit of $\left(\frac{n}{n+1}\right)^n$
69717
Find limit of recursive sequence $a_{n+1} =\sqrt{2+ \sqrt{a_n} }.$
58144
Solve the recurrence relation:$ T(n) = \sqrt{n} T \left(\sqrt n \right) + n$
55485
Recursive Function - $f(n)=f(an)+f(bn)+n$
68725
Find expression for : $ S_n =\sum_{i=1}^{n} \frac{i}{i^4+i^2+1} $
107098
Find an explicit formula for the recurrence $a_n = n(a_{n-1} + a_{n-2})$ knowing that $ a_0=1$ and $a_1=2$.
40227
Compute $\lim\limits_{n\to\infty}n^2\left(\left(1+\frac1{n+1}\right)^{n+1}-\left(1+\frac1n\right)^n\right)$
33492
Determine the recurrence formula
119278
The number $\frac{1}{\sqrt{5}}\left[\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^n\right]$ is always an integer
95718
Computing $ \lim_{n\rightarrow \infty}\left(\frac{1^n+2^n+\cdots \cdots +n^n}{n^n}\right)$
133070
Finding a closed form expression for the recurrence relation $a(n,k+1)=(k+1)^n+\sum_{m=1}^k {k+1\choose m}a(n,m)$
83346
Finding a closed form $x_n$ for the recurrence relation $x_{n+2} = px_{n+1} + qx_n + r$
89771
$\frac{1}{s-1}+\sum_{n=1}^{\infty}\left[\frac{1}{n^s}+\frac{1}{s-1}\left(\frac{1}{(n+1)^{s-1}} - \frac{1}{n^{s-1}}\right)\right]$
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$