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RRL
  • Member for 8 years, 1 month
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46 votes

The math behind Warren Buffett's famous rule – never lose money

32 votes

Prove $\lim_{n \to \infty} \frac{\ln(n)}{n}=0$ without L'Hospital's Rule

27 votes

Integrability of Thomae's Function on $[0,1]$.

20 votes
Accepted

A nonnegative random variable has zero expectation if and only if it is zero almost surely

18 votes

Why do some mathematical ideas seem counter-intuitive?

18 votes

Proving that $\gamma = \int_{0}^{1} \!\!\int_{0}^{1} \!\frac{x - 1}{(1 - x y) \log(x y)} \, \mathrm{d}{x} \, \mathrm{d}{y} $.

17 votes
Accepted

Proof that if $f$ is integrable then also $f^2$ is integrable

17 votes

Geometric mean of reals between 0 and 1

17 votes
Accepted

How to compute the pade approximation?

16 votes
Accepted

Uncorrelated but not independent random variables

15 votes

How to evaluate the sum $\sum_{k=2}^{\infty}\log{(1-1/k^2)}$?

15 votes

How to show that $\lim_{n\to \infty} \frac{a_1 +a_2 + \cdots + a_n}{n} = 0?$

15 votes
Accepted

Convergence $ \sum \frac{\sin \sqrt{n}}{n^{3/2}}, \quad \sum \frac{\sin n}{\sqrt{n}}, \quad\sum \frac{\sin \sqrt{n}}{n^{3/4}} $

15 votes
Accepted

Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$

14 votes
Accepted

Numerical Integration for integrable singularity

14 votes

On the convergence of $\sum_{n = 1}^\infty\frac{\sin\left(n^a\right)}{n^b}$

13 votes

Can someone explain in general what a central difference formula is and what it is used for?

13 votes
Accepted

Proof of connection between improper Riemann Integral and Lebesgue integral

12 votes
Accepted

Evaluate the limit $\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}\left(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n}}\right)$

12 votes
Accepted

Evaluating a Lebesgue Integral

12 votes

Deriving Taylor series without applying Taylor's theorem.

12 votes
Accepted

Riemann-Stieltjes integral of unbounded function

12 votes
Accepted

Is $\sum_{n=2}^{\infty}\frac{(-1)^n}{\sqrt n+(-1)^n}$ convergent?

12 votes
Accepted

Proof every convex function is continuous (Problem 10 Convex Functions Spivak)

12 votes

Riemann integral on a single point

11 votes
Accepted

If a sequence grows too fast, then its harmonic sum cannot be rational

11 votes
Accepted

Proving that the iterated limit and the two dimensional limit are same

11 votes
Accepted

How to deal with an indefinite L'Hôpital operation

11 votes

Showing that $\sup\{|f(x)-f(y)|, x,y\in X\}= \sup \ f - \inf \ f$

11 votes

Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$

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