How to show that the $\sum_{i=1}^{n}|A[i]-x|$ is minimal for $x=m$ with median $m$?
7740
The median minimizes the sum of absolute deviations (the $ {\ell}_{1} $ norm)
114575
If $\sum_{i=1}^k \dim F_i > n(k-1)$ then $\cap_{i=1}^k F_i \neq \{0\}$
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
151757
Simplify $\sum_{i=0}^{N/2}{N-i\choose i}$
111075
Deriving of formula for finding the length of median
122149
How to prove that $\sum_{i<j}(X_i-X_j)^2=n\sum_{i=1}^{n}(X_i-\bar{X})^2$
123190
Joint distribution of $\min(X_1,\ldots,X_n)$ and $\max(X_1,\ldots,X_n)$.
155828
How do I show that $A$ and $A^T$ are similar, given that the minimal polynomial of $A$ splits over $\mathbb{F}$?
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
65235
Show that if $\sum_na_n=\infty$ and $a_n\downarrow 0$ then $\sum\limits_n\min(a_{n},\frac{1}{n})=\infty$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
91081
Prove that, for every natural n, $\sum_{d|n} \frac{\mu(d)}{d}=\prod_{p|n}(1-\frac{1}{p})$
78471
Closure of $\{\frac{1}{n}\}:=M$
103744
Minimal $ab$ for Rational Number $a/b$ in an Interval
75349
Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$
78684
If $\sum_na_n=\infty$ and $a_n\downarrow 0$ then $\sum\limits_n\min(a_{n},\frac{1}{n})=\infty$