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Derek Jennings

England, United Kingdom

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Top Questions
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86
Ways to evaluate $\int \sec \theta \, \mathrm d \theta$
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61
Prove $0! = 1$ from first principles
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34
Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)
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33
Which is correct: “one or more is” or “one or more are”?
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32
Proving $\prod_{j=1}^n \left(4-\frac2{j}\right)$ is an integer
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30
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
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26
Why is $\pi $ equal to $3.14159…$?
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25
Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$
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25
Summing $\frac{1}{e^{2\pi}-1} + \frac{2}{e^{4\pi}-1} + \frac{3}{e^{6\pi}-1} + \cdots \text{ad inf}$
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24
Formerly good at math, but after 12 years I've lost most of my skills. Now I need them once again. Any advice to grow them back?
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24
Common misconceptions about math
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20
why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$
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20
Erroneous numerical approximations of $\zeta\left(\frac{1}{2}\right)$?
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18
Calculate $\pi$ precisely using integrals?
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18
How to compute the series $\sum_{n=0}^\infty q^{n^2}$?
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18
Which one result in mathematics has surprised you the most?
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16
Is there a proof that $\pi$ is an irrational number?
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16
Puzzle: digit $x$ appears $y$ times on this piece of paper…
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15
What is the importance of the Collatz conjecture?
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15
Proving $ \frac{\sigma(n)}{n} < \frac{n}{\varphi(n)} < \frac{\pi^{2}}{6} \frac{\sigma(n)}{n}$
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15
List of interesting math videos / documentaries
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15
Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$
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14
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
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13
$k^{2}+(k+1)^{2}$ being a perfect square for infinitely many $k$
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13
Computing $\sum_{m \neq n} \frac{1}{n^2-m^2}$
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12
Fermat's Last Theorem - Special Case of Sophie Germain Primes
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12
How to prove the equality $\sum_{j=0}^n (x)^j (-1)^{n-j} \left\{{n \atop j}\right\} = x^n$?
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12
Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$
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12
Nth derivative of a function: I don't know where to start
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12
Why is $\tau(n) \equiv \sigma_{11}(n) \pmod{691}$?
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