Skip to main content
VIVID's user avatar
VIVID's user avatar
VIVID's user avatar
VIVID
  • Member for 4 years, 3 months
  • Last seen this week
32 votes
Accepted

Let $a = \frac{1 + \sqrt{2009}}{2}$ . Find the value of $(a^3 - 503a - 500)^5$ .

16 votes
Accepted

How to calculate $ \left| \sin x \right| $ derivative in a more elegant way?

13 votes
Accepted

How many subsets of $\{1,2,...,n\}$ do not contain three consecutive integers?

13 votes
Accepted

Evaluate $\lim\limits_{n\to\infty}\frac{1\cdot3+2\cdot4+\dots+n(n+2)}{n^3}.$

10 votes
Accepted

Intuition on the concept of bounding a sum

10 votes
Accepted

How to read and execute $\sum_{1 \leq \ell <m<n} \frac{1}{5^{\ell}3^{m}2^{n}}$

9 votes

Convergence of $\sum_{n=0}^{\infty} \frac{4^n}{3^n+7^n}$

9 votes

How to solve $x^4-2x^3-x^2+2x+1=0$?

9 votes
Accepted

Find $\int_0^1 \frac{f(x)}{\sqrt{1+x^2}}dx$

8 votes
Accepted

Prove that $\int_{0}^{\infty} \frac{\zeta(\pi \cdot s) - \zeta(e \cdot s)}{ \zeta(\pi \cdot s) \zeta(e \cdot s) \cdot s} = 3 + \ln(\frac{1}{\pi^3}) $

8 votes
Accepted

Show that the inequality $\left|\int_{0}^{1} f(x)\,dx\right| \leq \frac{1}{12}$ holds for certain initial conditions

8 votes
Accepted

Solving $\cos(z) = \frac{5}{2}$

7 votes

If $A^m = 0$, then $\mbox{rank}(A) \leq \frac{m-1}{m}{n}$

7 votes

Solving the system $3a=(b+c+d)^3$, $3b=(c+d+e)^3$, ..., $3e=(a+b+c)^3$ for real $a$, $b$, $c$, $d$, $e$

7 votes
Accepted

Ex.1.1 9 from topology without tears

7 votes
Accepted

All real numbers $(p,q)$ such that $|\sqrt{1-x^{2}}-p x-q| \leq \frac{\sqrt{2}-1}{2}$ holds for every $x \in[0,1]$

7 votes
Accepted

A function with a condition

7 votes
Accepted

How to evaluate $\lim\limits_{x\to \infty}\frac {2x^4-3x^2+1}{6x^4+x^3-3x}$?

6 votes
Accepted

How can I prove that $\sum_{n=1}^\infty \dfrac{n^4}{2^n} = 150 $?

6 votes

How is this a function? - Analysis.

6 votes
Accepted

Let $f:[0,2]\to \mathbb{R}$ be a continuous function with no roots. Prove that the function is not surjective and $f(0)\cdot f(2)>0$

6 votes

Solving a super basic inequality

6 votes
Accepted

Question on binomial theorem: Find the term independent of $x$ in the expansion of $(2+x)\left(2x+\frac{1}{x}\right)^5$

6 votes
Accepted

Evaluate $\int_{1}^{e} x^{n} \ln x \mathrm{d} x$

6 votes

Simplify $\sum^{20}_{k=10} k\binom{k-1}{9}$.

6 votes
Accepted

Need help with this proof via induction

6 votes

Evaluate $\sum_{n=1}^{50}n\cdot n!$.

5 votes
Accepted

If $A$ is an orthogonal matrix with $|A|=-1$, show that $|I-A|=0$

5 votes

Sum of triangular number

5 votes
Accepted

Prove that if x,y,z are positive integers such that $x^3+y^3+z^3=3(x+y+z+xyz)$ then they must be consecutive numbers

1
2 3 4 5
12