Proving that the function $f(N)=\sum_{n=1}^N \cos(n^2)$ is unbounded
30953
Is $\sum_{k=1}^{n} \sin(k^2)$ bounded by a constant $M$?
142812
Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$
133882
$\lim_{n\to \infty }\cos (\pi\sqrt{n^{2}-n})$ - second battle
5650
Show $\ln2 = \sum_\limits{n=1}^\infty\frac1{n2^n}$
17779
Proving the Limit of a Sequence of without the Dominated Convergence Theorem
162
Determine the convergence of $ \sum_{n=1}^{\infty}\left[1-\cos\left(1 \over n\right)\right] $
140614
Show that $\sum^\infty_{n=m}\frac{1}{n^2} = O(\frac{1}{m})$
26388
proof that function is constant
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
147203
How to show that $\lim_{n\to\infty}\left\{f(c+\frac{1}{n^2})+f(c+\frac{2}{n^2})+\cdots+f(c+\frac{n}{n^2})-nf(c)\right\}=\frac{1}{2} f'(c)$
95353
Does $\sum_{n=1}^\infty \frac{\cos{(\sqrt{n})}}{n}$ converge?
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
24407
How to prove the Fibonacci sum $\sum \limits_{n=0}^{\infty}\frac{F_n}{p^n} = \frac{p}{p^2-p-1}$
114031
Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
37158
upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$
133451
To show that ${x_n}$ is convergent where $|x_{n+1} - x_n|< \frac{1}{n^2}$
85626
prove $\sum_{i=1}^{n}(x_i-\bar{x})^2\lt\sum_{i=1}^{n}(x_i-a)^2$