User E.H.E - Mathematics Stack Exchange

22 votes

Exact Sum of Series

answered Dec 2, 2015 at 21:05

18 votes

Why is this integration method not valid?

answered May 19, 2019 at 20:42

14 votes

Value of this convergent series: $\frac{1}{3!}+\frac2{5!}+\frac3{7!}+\frac{4}{9!}+\cdots$

answered Jul 22, 2016 at 17:17

12 votes

Different ways to prove $\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}$ (the Basel problem)

answered Jun 24, 2016 at 22:37

11 votes

Accepted

How do we integrate $(e^x + 2x)^2$?

answered Apr 15, 2015 at 22:14

11 votes

Accepted

Prove or disprove: $\sum_{k=1}^{\infty}\frac{\sqrt{k+1}-\sqrt{k}}{k\sqrt{k}}$ is convergent

answered Sep 20, 2016 at 14:58

10 votes

Limits to infinity of a factorial function: $\lim_{n\to\infty}\frac{n!}{n^{n/2}}$

answered Nov 19, 2016 at 17:16

10 votes

Accepted

Finding $\lim_{n\rightarrow \infty }\left(1-\frac{1}{n^2}\right)^n$

answered Jun 4, 2015 at 23:02

10 votes

Accepted

Why does $k^2+4k+4$ become $(k+2)^2$?

answered Oct 3, 2015 at 9:38

9 votes

How do I prove that $x^2 + y^2 = (x + y) ^2 – 2xy$ geometrically/intuitively?

answered May 8, 2015 at 22:12

9 votes

Accepted

Proving $\int_{0}^{1}\sqrt{\frac{1-x}{1+x}}dx=\frac{π}{2}-1$

answered Apr 18, 2015 at 3:23

9 votes

Accepted

Solve $2x(1+\frac{1}{x^3})+7(1+\frac{1}{x})=0$ without cubic formulas and such

answered Sep 27, 2016 at 15:17

9 votes

Is there any difference in solutions between $x^7-1^7=0$ and $x^7-1=0$?

answered Aug 25, 2016 at 18:05

8 votes

Easier way to calculate the derivative of $\ln(\frac{x}{\sqrt{x^2+1}})$?

answered Sep 19, 2016 at 21:26

8 votes

Limit of the sequence $\lim_{n\to\infty}{\sqrt[n]{4^n + 5^n}}$

answered Oct 5, 2016 at 18:31

8 votes

How to find the limit using L'Hôspital's Rule

answered Oct 10, 2016 at 22:05

8 votes

How to solve this equation for $x$?$\left(\sqrt{2-\sqrt{3}}\right)^x + \left(\sqrt{2+\sqrt{3}}\right)^x = 2$

answered Jun 18, 2015 at 17:32

8 votes

Accepted

Does the series: $\sum_{n=1}^\infty \frac{2n+1}{n^2(n+1)^2}$ converge?

answered Jun 19, 2015 at 13:12

8 votes

What is the value of $\frac11+\frac13-\frac15-\frac17+\frac19+\frac1{11}-\dots$?

answered Apr 17, 2019 at 12:30

7 votes

Accepted

finding out if two vectors are perpendicular or parallel

answered Jun 13, 2015 at 17:46

7 votes

Accepted

Proof $\sum_{n=0}^\infty \frac{n^2+3n+2}{4^n} = \frac{128}{27}$

answered Oct 5, 2016 at 20:04

6 votes

Accepted

Find the Maclaurin Series for $\frac{x}{x^2 + 1}$

answered Oct 3, 2016 at 11:01

6 votes

Need to simplify ratio test: $\frac{(2(k+1))!}{(2k)!} $

answered Sep 3, 2016 at 12:27

6 votes

Calculate: $\frac{1}{2! \cdot 2} + \frac{1}{4! \cdot 4} + \frac{1}{6! \cdot 8} + \frac{1}{8! \cdot 16} + ...$

answered Sep 8, 2016 at 10:56

6 votes

Test of being a rational number for $(1-\frac13+\frac15-\frac17+\cdots)/(1+\frac14+\frac19+\frac1{16}+\cdots)$

answered Aug 24, 2016 at 17:25

6 votes

How to solve $4^x+\sin(x)=10$

answered Jun 5, 2015 at 20:29

6 votes

Finding the angle between two line equations

answered May 6, 2015 at 0:35

6 votes

Accepted

How to differentiate $x^2-|x^3|$?

answered Apr 14, 2015 at 23:55

6 votes

Accepted

Taylor series about 0 for $\frac{x^{2}}{e^{2x}}$

answered Sep 18, 2015 at 10:05

6 votes

Limit for $(\frac{n}{n+1})^n$ to infinity

answered Sep 30, 2015 at 18:07

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788 Answers

Exact Sum of Series

Why is this integration method not valid?

Value of this convergent series: $\frac{1}{3!}+\frac2{5!}+\frac3{7!}+\frac{4}{9!}+\cdots$

Different ways to prove $\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}$ (the Basel problem)

How do we integrate $(e^x + 2x)^2$?

Prove or disprove: $\sum_{k=1}^{\infty}\frac{\sqrt{k+1}-\sqrt{k}}{k\sqrt{k}}$ is convergent

Limits to infinity of a factorial function: $\lim_{n\to\infty}\frac{n!}{n^{n/2}}$

Finding $\lim_{n\rightarrow \infty }\left(1-\frac{1}{n^2}\right)^n$

Why does $k^2+4k+4$ become $(k+2)^2$?

How do I prove that $x^2 + y^2 = (x + y) ^2 – 2xy$ geometrically/intuitively?

Proving $\int_{0}^{1}\sqrt{\frac{1-x}{1+x}}dx=\frac{π}{2}-1$

Solve $2x(1+\frac{1}{x^3})+7(1+\frac{1}{x})=0$ without cubic formulas and such

Is there any difference in solutions between $x^7-1^7=0$ and $x^7-1=0$?

Easier way to calculate the derivative of $\ln(\frac{x}{\sqrt{x^2+1}})$?

Limit of the sequence $\lim_{n\to\infty}{\sqrt[n]{4^n + 5^n}}$

How to find the limit using L'Hôspital's Rule

How to solve this equation for $x$?$\left(\sqrt{2-\sqrt{3}}\right)^x + \left(\sqrt{2+\sqrt{3}}\right)^x = 2$

Does the series: $\sum_{n=1}^\infty \frac{2n+1}{n^2(n+1)^2}$ converge?

What is the value of $\frac11+\frac13-\frac15-\frac17+\frac19+\frac1{11}-\dots$?

finding out if two vectors are perpendicular or parallel

Proof $\sum_{n=0}^\infty \frac{n^2+3n+2}{4^n} = \frac{128}{27}$

Find the Maclaurin Series for $\frac{x}{x^2 + 1}$

Need to simplify ratio test: $\frac{(2(k+1))!}{(2k)!} $

Calculate: $\frac{1}{2! \cdot 2} + \frac{1}{4! \cdot 4} + \frac{1}{6! \cdot 8} + \frac{1}{8! \cdot 16} + ...$

Test of being a rational number for $(1-\frac13+\frac15-\frac17+\cdots)/(1+\frac14+\frac19+\frac1{16}+\cdots)$

How to solve $4^x+\sin(x)=10$

Finding the angle between two line equations

How to differentiate $x^2-|x^3|$?

Taylor series about 0 for $\frac{x^{2}}{e^{2x}}$

Limit for $(\frac{n}{n+1})^n$ to infinity