Prove or disprove: $\big\{\sum_{i=1}^n x_i^2 = 1\big\}$ is convex.
52231
Prove or disprove {$\sum_{i=1}^n x_i^2 = 1$} is convex
122942
Prove that if $\sum |a_{n}|$ converges then $\sum a_{n}^{2}$ converges
119668
How prove this inequality: $\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge n\sum_{i=1}^{n}|x_{i}|$?
123732
Proving that the maximum of two convex functions is also convex
25017
Why is every $p$-norm convex?
125175
convexity proof of a function including ln and sums
102959
Show that $f$ is convex if and only if $f\left( \sum_{i=1}^m\lambda_ix_i \right) \leq \sum_{i=1}^m\lambda_if(x_i)$
11942
show that $x$ is in $\ell^1$ if $\sum x_ny_n$ is convergent for all $y=(y_n)\in{c_0}$
54900
How to prove $|\sum_{i=1}^n a_i|\le \sqrt{n} \sqrt{\sum_{i=1}^n a_i^2}$
143113
Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$
135867
$f(x)=x^3$ is convex nor concave without to derivate
32611
Is the trace of inverse matrix convex?
16749
Let $A_i= \left \{...,-2,-1,0,1,...,i \right\}$. Find $\bigcup_{i=1}^{n} A_i$ and $\bigcap_{i=1}^{n} A_i$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
40438
Proving that closed (and open) balls are convex
77510
$\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$
71829
Is closure of convex subset of $X$ is again a convex subset of $X$?