Robert Z's user avatar
Robert Z's user avatar
Robert Z's user avatar
Robert Z
  • Member for 8 years, 4 months
  • Last seen this week
81 votes
Accepted

Every polynomial with real coefficients is the sum of cubes of three polynomials

47 votes
Accepted

Value of $(\alpha^2+1)(\beta^2+1)(\gamma^2+1)(\delta^2+1)$ if $z^4-2z^3+z^2+z-7=0$ for $z=\alpha$, $\beta$, $\gamma$, $\delta$

43 votes
Accepted

Intuitive reason for why $\left(\displaystyle\sum_{i=0}^n i\right)^2 = \displaystyle\sum_{i=0}^n i^3$

34 votes

Does an increasing sequence of reals converge if the difference of consecutive terms approaches zero?

30 votes
Accepted

Polynomial cannot have all roots real?

30 votes

Prime number construction game

26 votes

Question about partial fractions with irreducible quadratic factors

25 votes

What will be the value of the following determinant without expanding it?

25 votes
Accepted

How can I find the equation of a circle given two points and a tangent line through one of the points?

23 votes
Accepted

Third degree Taylor series of $f(x) = e^x \cos{x} $

22 votes
Accepted

Prove or disprove convergence of a series

20 votes
Accepted

How to evaluate the limit where something is raised to a power of $x$?

20 votes
Accepted

Can a function have a derivative where it has no value?

18 votes
Accepted

Is there a name/notation for the sum of the powers in a prime factorization

18 votes

Find $\int_1^\infty \frac{\{x\}}{x(x+1)}dx,$ where $\{x\}$ means $x - \lfloor x \rfloor$.

18 votes
Accepted

Evaluate an integral using Laplace transform

17 votes
Accepted

Evaluate $\int_0^1(x\ln(x))^{50}dx$

17 votes

How to find the sum of $1+(1+r)s+(1+r+r^2)s^2+\dots$?

17 votes
Accepted

Does $\sum_{n=1}^\infty \frac{\cos{(\sqrt{n})}}{n}$ converge?

17 votes
Accepted

Calculate the probability of getting a total of 6 in three throws of a die

16 votes
Accepted

On the Taylor coefficients of $\arcsin^3$

16 votes
Accepted

How to show that a large given integer isn't a square number by using mod?

15 votes

Compute $\int\limits_2^4\frac{f(x)}{xf(x)+xf(\frac8x)}\mathrm dx$

15 votes
Accepted

A series with Fibonacci numbers and the golden ratio

14 votes
Accepted

Minimum value of $2^{\sin^2x}+2^{\cos^2x}$

14 votes
Accepted

Sum of reciprocals of the perfect powers

14 votes

Proving $\int_0^1\frac{\vert f(x)\rvert^2}{x^2}\,\mathrm dx\le4\int_0^1{\vert f'(x)\rvert^2}\,\mathrm dx$ when $f\in\mathcal C^1([0,1])$ and $f(0)=0.$

14 votes

$\int_{0}^{\infty}\tan^{-1}\left(\frac{2x}{1+x^2}\right)\frac{x}{x^2+4}dx$

14 votes
Accepted

Find the minimum of $(1+a^2)(1+b^2)(1+c^2)$ where $a,b,c\geq 0$

14 votes

Find the height of a bar, given the lengths of shadows cast by it and another bar

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