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Pen and Paper
  • Member for 2 years, 10 months
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4 votes
1 answer
268 views

A question on proving that $e$ is irrational

4 votes
1 answer
108 views

Binomial/combinatorics summation proof question

4 votes
6 answers
260 views

Fastest way to find $\cos{6\theta}$ or higher in terms of powers of $\cos$

4 votes
2 answers
105 views

Don't understand a line for the proof of $\displaystyle \sum_{1≤k≤n}\frac{\sin{kx}}{k}≥0$

4 votes
1 answer
221 views

What am I doing wrong with this Euler substitution?

4 votes
2 answers
85 views

Finding the value of $\frac{1}{z_1-z_2}+\frac{1}{z_2-z_3}+...+\frac{1}{z_7-z_1}$

3 votes
2 answers
144 views

How to show that $\left(\sqrt{\binom{n}{1}}+\sqrt{\binom{n}{2}}+...+\sqrt{\binom{n}{n}}\right)^2≤n(2^n-1)$?

3 votes
1 answer
357 views

Finding the sum of $\cos{x}+2\cos{2x}+...+n\cos{nx}$ [duplicate]

3 votes
2 answers
236 views

How to evaluate an integral that comes out as undefined

3 votes
0 answers
45 views

Probability multi-choice question

3 votes
4 answers
357 views

Finding the minimum value of $|z-3+i|$ given $z$ satisfies $\arg{(z-2i)}=\frac{\pi}{6}$

3 votes
2 answers
115 views

Find the centre and radius of $\arg{\left(\frac{z-(5+7i)}{z-(7+9i)}\right)}=\frac{\pi}{4}$?

3 votes
1 answer
183 views

Motivation behind this proof of the Basel problem?

2 votes
2 answers
252 views

Golden ratio in complex number squares

2 votes
1 answer
52 views

Where did I go wrong in finding the sum of $1+2k+3k^2+...+nk^{n-1}$ using Abel's formula

2 votes
2 answers
112 views

Finding the sum of $1+4k+9k^2+...+n^2k^{n-1}$

2 votes
1 answer
69 views

How do I apply some extended sketching techniques?

2 votes
0 answers
74 views

Complex and real roots of a polynomial

2 votes
2 answers
223 views

Describe the locus of $w$ if $w=\frac{1-z}{1+z}$ and $z=1+iy$ (i.e $z$ is a complex number that moves along the line $x=1$)

2 votes
1 answer
437 views

Does this proof that two spheres only have one point of contact even make sense?

2 votes
2 answers
121 views

What am I doing wrong to finding the perpendicular distance between a point and a plane?

2 votes
3 answers
160 views

Why does $\displaystyle\int_{-\pi}^{\pi}\frac{\sec^2{x}}{2\tan^2{x}+1} dx$ evaluate to be $0$ even when the graph is always positive?

2 votes
1 answer
66 views

Checking solution for complex numbers such that $|z_1|=|z_1+z_2|=3$ and $|z_1-z_2|=3\sqrt{3}$.

1 vote
1 answer
87 views

Identity with roots of $\frac{x}{x-p}+\frac{x}{x-q}+\frac{x}{x-r}+(x-s)=0$.

1 vote
2 answers
104 views

Finding a closed form for $\int_1^e \frac{(\ln x)^n}{x^2} dx$

1 vote
1 answer
96 views

Solving $\sqrt[2k+1]{x+1}+\sqrt[2k+1]{x+2}+\sqrt[2k+1]{x+3}+...+\sqrt[2k+1]{x+n}=0$

1 vote
0 answers
20 views

Counter-intuitive result for resisted motion

1 vote
0 answers
110 views

Does this explanation for the volume of rotation about a horizontal line make sense?

1 vote
3 answers
101 views

If all the roots of $P(x)=x^3-\sqrt{27}x^2+bx-\sqrt{27}$ are real and positive, find the value of $b$ for $b>0$

1 vote
1 answer
309 views

Mapping a hemisphere onto the unit circle