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12 votes
Accepted

Use Mean value theorem to prove the following inequality

6 votes
Accepted

In a Hilbert space $x_n \overset{\text{w}}{\to} x$ and $y_n \to y$. Prove $\langle x_n, y_n \rangle \to \langle x, y \rangle$

5 votes
Accepted

for $p>0$, when does this integration:$\int_0^{\infty} x^pe^{-x^8\sin^2x}dx$ converge?

4 votes
Accepted

Prove inequality with logarithms

4 votes

Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?

4 votes

Elliptic Matrix

4 votes

How to prove this rank inequality?

3 votes
Accepted

Prove the inequality...

3 votes

How to find the length of a side using properties of triangle?

3 votes

The limit of the function with $\frac{\infty}{0}$ and $\frac{0}{\infty}$

3 votes

Is the sequence $\{\{\log(n!)\}\}_n$ dense in $[0,1]$?

3 votes

Show $\sum \frac{xy}{xy+x+y} \le \frac{6+x^2+y^2+z^2}{9}$

3 votes
Accepted

Real analysis : Problem related to inverse

2 votes
Accepted

$k\sum v_i v_i^T-\big(\sum v_i\big)\big(\sum v_i^T\big)\succeq 0$

2 votes

How to show that $\sum_{n\ge10}\frac{(\log n)^2(\log\log n)}{n^2}$ converges

2 votes
Accepted

The integral of $f(0.x_1 x_2 \cdots)= 0.\sigma(x_1)\sigma(x_2)\cdots$

2 votes

nth root of Bernoulli numbers

2 votes

How to calculate $\lim\limits_{n \to \infty } \left(\frac{n+1}{n-1}\right)^{3n^{2}+1}$?

2 votes

Integral inequality 4

2 votes

How to show $\lim_{n \rightarrow \infty} \frac{[a^{n+1}]}{[a^n]}=a$?

2 votes

Is it $\lvert\max\limits_a f(a) - \max\limits_a g(a) \rvert \leq \max\limits_a \lvert f(a) - g(a)\rvert$ true?

2 votes
Accepted

Prove $p\mid\frac{x^{a}-1}{x-1}$ using Fermat's little theorem

2 votes

Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$

2 votes

The $\frac{\sin x}x$ limit and the floor function

2 votes

Proving that all solutions of $(1+z)^n=z^n$ have $\mathrm{Re}(z)=-\frac{1}{2}$

2 votes

Generating function for counting compositions of $n$

2 votes
Accepted

Proof that the gamma function has a minimum between $x=1$ and $x=2$?

1 vote

$\lim_{n \to \infty }n\int_{0}^{\pi}\left \{ x \right \}^{n}dx$

1 vote

Why are those equations true?

1 vote

Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$