if $f(x) \sim g(x)$ is $ \sum f(k) \sim \sum g(k)$
53443
Does $a_n \sim b_n$ imply $\sum_n a_n \sim \sum_n b_n$ for $a_n, b_n>0$?
153612
Finding $g_i:\mathbb{R}^n\to\mathbb R$ s.t $f(x)=\sum\limits_{i=1}^nx_i\cdot g_i(x)$
139531
If $f'/f=g'/g$ at every $1/n$ then $f=kg$ for some complex number $k$
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
6450
Show $\mathbb{E}[f(X)g(X)] \geq \mathbb{E}[f(X)]\mathbb{E}[g(X)]$ for $f,g$ bounded, nondecreasing
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
44706
Behavior of $\sum a_n x^n$ given $\sum |a_n - a_{n-1}| < \infty$
26424
If $f(x)<g(x)$ prove that $\lim f(x)<\lim g(x)$
133755
Is true that $\sum_{k=1}^n\frac{[kx]}{k}\leq[nx]$, for every $x\in\mathbb{R}$ and for every $n\in\mathbb{Z}^+$?
14282
$X/{\sim}$ is Hausdorff if and only if $\sim$ is closed in $X \times X$
66758
$f_n:[0,1]\to [0,1]$ continuous, $f_n\to f$ uniformly, prove: ${\frac1n}\sum_{k=1}^{n}{f_k} \to f$ uniformly
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
82935
Prove that f∈Θ(g)if and only ifO(f) =O(g).
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
10859
Prove $\sup(f+g) \le \sup f + \sup g$