sum of absolute differences $|\sigma(i)-i|$ is even
96585
Sums and permutation
156564
Prove the identity $\sum_{{{\underset{k-even}{k=0}}}}^{n}{n \choose k}2^{k}=\frac{3^{n}+(-1)^{n}}{2}$
119381
Sum of even numbers errors
47644
Inequality involving rearrangement: $ \sum_{i=1}^n |x_i - y_{\sigma(i)}| \ge \sum_{i=1}^n |x_i - y_i|. $
143857
How to prove absolute summability of sinc function?
28332
Proof of $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$
123267
Proving that even numbers equal the sum of two odd numbers.
119552
Summing Finitely Many Terms of Harmonic Series: $\sum_{k=a}^{b} \frac{1}{k}$
349
Prove $| \sum_{i \leq n} \frac{\mu(i)}{i} | \leq 1$
41930
Mean of $ \sum (X_i - \bar{X})^2$
46775
If $\sigma_n=\frac{s_1+s_2+\cdots+s_n}{n}$ then $\operatorname{{lim sup}}\sigma_n \leq \operatorname{lim sup} s_n$
132595
$\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
123757
Proving a summation inequality with induction
72256
Prove there exists two sub-sets of indices $I,J\subseteq [2n]$ such that $\sum_{i\in I}a_i=\sum_{j\in J}b_j$
28151
Prove that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ converges absolutely
109180
Deriving Sum of a Geometric Progression
115258
Find all positive integers $n$ such that $\phi(n)+\sigma(n)=2n$.