Skip to main content
Khosrotash's user avatar
Khosrotash's user avatar
Khosrotash's user avatar
Khosrotash
  • Member for 10 years, 7 months
  • Last seen this week
56 votes
Accepted

Sum of series $\sum \limits_{k=1}^{\infty}\frac{\sin^3 3^k}{3^k}$

30 votes

Other Idea to show an inequality $\dfrac{1}{\sqrt 1}+\dfrac{1}{\sqrt 2}+\dfrac{1}{\sqrt 3}+\cdots+\dfrac{1}{\sqrt n}\geq \sqrt n$

27 votes

Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?

27 votes

Congruence Arithmetic Laws, e.g. in divisibility by $7$ test

23 votes
Accepted

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

21 votes

How to find length of a part of a curve?

19 votes

Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction

14 votes

Determine whether the series converges or diverges.

10 votes
Accepted

$ \lim_{n \rightarrow \infty} n \left( \frac{1}{(n+1)^2} + \frac{1}{(n+2)^2} + \cdots + \frac{1}{(2n)^2} \right)$ as Riemann sum?

8 votes
Accepted

How can $n^4 + 2n^3 + n^2$ be written in sum notation?

8 votes
Accepted

If $a,b$ are roots of $3x^2+2x+1$ then find the value of an expression

8 votes

Integrate over a discontinuity

8 votes

How prove $\bigl(\frac{\sin x}{ x}\bigr)^{2} + \frac{\tan x }{ x} >2$ for $0 < x < \frac{\pi}{2}$

8 votes
Accepted

Solve $\sqrt x = x/2$.

8 votes
Accepted

Find $x\in \Bbb Z$ such that $x=\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}$

7 votes
Accepted

$\frac {1} {ab} + \frac {1} {ac} + \frac {1} {ad} + \frac {1} {bc} + \frac {1} {bd} + \frac {1} {cd}$

7 votes

Sum of cosines of complementary/suplementary angles

6 votes
Accepted

Solving inequalities on both sides with complex numbers

6 votes
Accepted

How do we find the $n+2$th term of the series $1 + (3+5) + (7+9+11)+\dots$?

6 votes

Why is a repeating decimal a rational number?

6 votes

Looking for $\sum_{n=1}^{\infty}\frac{1}{F_{n}F_{n+2}}$

6 votes
Accepted

Explain why the graph of $y=\frac{4x}{x^2+1}$ and $y=2\sin(2\arctan x)$ are the same.

6 votes
Accepted

Riemann Sums - Prove $\lim_{n\to\infty} \frac{1}{n} \sqrt[n]{n!} = 1$

6 votes
Accepted

Series $\sum_{k=1}^n\frac{\tan\frac x{2^k}}{2^{k-1} \cos\frac x{2^{k-1}}}$

6 votes

Other idea to find range of $y=x+\frac{1}{x-4}$

6 votes

Domain and range of a floor function

6 votes

Partial fractions decomposition of ${\frac{2x}{(x+2)^2}}$

6 votes
Accepted

Easy way to find the partial fraction

6 votes

Why is $\frac{d}{dx}\ln |x|=\frac 1x$

6 votes
Accepted

Given $x^2 - 3x +6=0$ find $x^4$ in terms of $x$.

1
2 3 4 5
34