User Khosrotash

55 votes

Accepted

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

answered Jan 23, 2017 at 7:51

30 votes

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

answered Feb 18, 2017 at 0:09

27 votes

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

answered Jul 18, 2015 at 0:13

26 votes

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

answered Nov 1, 2013 at 17:07

23 votes

Accepted

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

answered Apr 14, 2015 at 21:02

21 votes

How to find length of a part of a curve?

answered Feb 3, 2017 at 17:16

19 votes

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

answered Feb 10, 2017 at 11:20

14 votes

Determine whether the series converges or diverges.

answered Jul 1, 2017 at 19:56

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?

answered Jan 30, 2017 at 3:56

8 votes

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

answered Dec 30, 2014 at 16:45

8 votes

Accepted

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

answered Jan 28, 2017 at 5:49

8 votes

Accepted

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

answered Jul 3, 2017 at 11:47

8 votes

Accepted

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

answered Aug 16, 2017 at 3:22

7 votes

Accepted

Solve $\sqrt x = x/2$.

answered Sep 6, 2014 at 12:06

7 votes

Sum of cosines of complementary/suplementary angles

answered Jul 28, 2015 at 22:05

7 votes

Integrate over a discontinuity

answered Jul 5, 2017 at 3:42

6 votes

Accepted

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

answered Jul 25, 2015 at 8:22

6 votes

Accepted

Solving inequalities on both sides with complex numbers

answered Jun 17, 2015 at 7:48

6 votes

Accepted

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

answered Oct 29, 2014 at 15:43

6 votes

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

answered Jun 5, 2014 at 12:07

6 votes

Accepted

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

answered Oct 9, 2016 at 10:34

6 votes

Accepted

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

answered Jul 22, 2017 at 5:30

6 votes

Accepted

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

answered Aug 26, 2017 at 5:38

6 votes

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

answered Sep 30, 2017 at 7:43

6 votes

Domain and range of a floor function

answered Oct 1, 2017 at 17:46

6 votes

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

answered Nov 10, 2017 at 14:38

6 votes

Accepted

Easy way to find the partial fraction

answered Mar 20, 2020 at 21:37

6 votes

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

answered Sep 27, 2020 at 6:01

6 votes

Accepted

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

answered Oct 10, 2020 at 5:22

5 votes

Why is a repeating decimal a rational number?

answered Nov 2, 2013 at 18:53

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935 Answers

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

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

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

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

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

How to find length of a part of a curve?

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

Determine whether the series converges or diverges.

$ \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?

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

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

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

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

Solve $\sqrt x = x/2$.

Sum of cosines of complementary/suplementary angles

Integrate over a discontinuity

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

Solving inequalities on both sides with complex numbers

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

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

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

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

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

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

Domain and range of a floor function

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

Easy way to find the partial fraction

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

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

Why is a repeating decimal a rational number?