uniform convergence of $f_n(x)=\left(\cos\frac{x}{\sqrt{n}}\right)^n$
106000
Determine if $f_n(x)= \big(\cos (\frac x {\sqrt n} )\big )^n $ converges pointwise or/and uniformly?
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
46830
Prove that the sequence $a_{n+1} =\frac{1}{2}\left(a_{n}+\frac{c}{a_{n}}\right)$ is convergent and find its limit
30167
Convergence of $\sqrt[n]{x^n+y^n}$ (for $x, y > 0$)
88147
Show that $g_n(x)=nf(x+1/n)-nf(x)$ converges uniformly to $f'$
26238
What values of alpha guarantee the convergence of $\sum _{n=0}^{\infty }\left( \frac {\alpha n} {n+1}\right) ^{n}$?
142645
$f_n$ converges uniformly on $[a,b]$ to some function $f$
43576
Convergence of $\sum _{n=1}^{\infty }\left\{ 1-n\log \frac {2n+1} {2n-1}\right\} $
69254
Which of the following series is uniformly convergent?
135110
Pointwise convergence of $h_n(x) = x^{1+\frac{1}{2n-1}}$
33965
Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$
125813
Convergence of $ \sum_{n=1}^\infty\left(\exp(\frac{(-1)^n}{n})-1\right)$?
35514
If $\{f_n\}$ converges uniformly and each $f_n$ is bounded, show that $\exists M>0$ s.t. $|f_n(x)| \leq M$
76756
A convergence proof: $\lim_{n\to\infty} \left(1+n^2\right)^{\frac1n}$
62892
Uniform convergence of $\sum_{n=1}^{\infty}\frac{1}{n(1+(x-n)^2)}$
144957
Uniform convergence of a function
25532
Determine if the convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ is uniform.