Is it true that $\lim_{n\to \infty}\sum_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n} = 0$?
104365
Evaluate: $\lim_{n\to\infty}\left({2\sqrt n}-\sum_{k=1}^n\frac1{\sqrt k}\right)$
32423
Convergence of $\sum _{k=1}^\infty (1-\frac{1}{k})^{k^2}$
28587
Show that $\sum\limits_{n=1}^\infty \frac {\sqrt{a_n}}{n}$ converges if $\sum\limits_{n=1}^\infty{a_n}$ does provided that $a_n>0$
158737
What is the value of the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n^2}$?
123108
Does the series $ \sum\limits_{n=1}^{\infty} \frac{1}{n^{1 + |\sin(n)|}} $ converge or diverge?
63165
Is this limit correct: $\lim_{x \to+\infty} \frac{\log_{2}(x-1)}{x} = 0$?
127627
Does $\sum^{\infty}_{n=1} n/(n-1)!$ converge to something?
110568
Does $\sum_{k=1}^{\infty}\ln(\frac{k}{k+1})$ converge/diverges??
98247
Is $ \sum\limits_{n=1}^\infty \frac{|\sin n|^n}n$ convergent？
112772
Is the series $\sum \limits_{n=1}^{\infty} \sin(n^2)$ convergent?
95353
Does $\sum_{n=1}^\infty \frac{\cos{(\sqrt{n})}}{n}$ converge?
49860
Determine the convergence of $\sum\limits_{n=2}^\infty \frac{\sqrt{n+1}}{n(n-1)}$
25852
Does the series $\sum_{n=1}^\infty$ ${\sqrt{n+1}-\sqrt{n}}\over n$ converge or diverge?
71798
$\lim_{n\to \infty}\frac{1}{n} \sum_{k=1}^n x_k =x\;$ given $\;\lim_{n\to \infty} x_n= x\;?$
85268
Convergence of $\sum_{n=1}^{\infty}{\sqrt[n]{n}-1 \over n}$
33965
Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$
47980
Infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log (n)}$