Why is sequence $(1+\frac{1}{n})^{n+1}$ descending?
92175
Given $y_n=(1+\frac{1}{n})^{n+1}$ show that $\lbrace y_n \rbrace$ is a decreasing sequence
146587
Why does the series $\sum_{n=1}^∞ \ln ({n \over n+1})$ diverges? And general tips about series and the logarithm
33419
If $a_n$ is a strictly increasing unbounded sequence, does $\sum_n \frac{a_{n+1} - a_n}{a_n}$ diverge?
3211
The sequence $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}, x_0>0$ is bounded?
25583
Show that the sequence $a_0 = 1$, $a_{n+1 }= \sqrt{2+a_n}$ is monotonically increasing
135927
Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$
35885
Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
5072
To evaluate limit of sequence $\left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
112595
Prove that the limit of this sequence is $\frac{1}{2}(1 + \sqrt{5})$
1869
Why does $\lim_{n\to\infty}(1+\frac{1}{n})^n = e$ instead of $1$?
48845
What Is The General Term Of These Sequences?
41445
Show that the sequence $a_n\leq a_{2n}+a_{2n+1}$ diverges
14836
A polynomial sequence
5797
Limit of the sequence $a_n=\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}$
110680
Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$
42300
Let the sequence be defined recursively $X_{n+1}=pX_{n}+q$ for p nonzero and $X_{1}$ arbitrary. In what conditions does the sequence converge?