Prove that $ \sum\limits_{n=1}^N \cos(2\pi n/N)= 0 $?
9479
$\sum \cos$ when angles are in arithmetic progression
157539
Prove: $\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits_{k=1}^{n}\sqrt{1+\frac{k}{n}}=\frac{2}{3}(2\sqrt{2}-1)$
2885
Prove that $\sum\limits_{i=1}^n 2i\binom{2n}{n-i}= n\binom{2n}{n}$
17157
Proving $\sum\limits_{k=1}^{n}{\frac{1}{\sqrt{k}}\ge\sqrt{n}}$ with induction
101017
What is the sum of $\sum\limits_{i=1}^{n}ip^i$?
7198
How can I show whether the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n(2+(-1)^n)} $ converges or diverges?
80277
How to show that $\lim \frac{1}{n} \sum_{i=1}^n \frac{1}{i}=0 $?
24575
How to prove that $ \sum_{n \in \mathbb{N} } | \frac{\sin( n)}{n} | $ diverges?
112772
Is the series $\sum \limits_{n=1}^{\infty} \sin(n^2)$ convergent?
54595
Prove $\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ = $\frac{(n-1)}{n}$ using induction.
143207
What is $\sum\limits_{i=1}^n \sqrt i\ $?
146047
Proving that $\cos(2\pi/n)$ is algebraic
123955
How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
89698
Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
107789
Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$
121071
Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
46353
Proof that $\cos(\pi/3)=1/2$