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2,197 Answers

newest activity votes
69
The sum of irrationals is irrational?
36
Crazy induction
35
Logic question: Ant walking a cube
32
Find all roots of $\,(x + 1)(x + 2)(x + 3)^2(x + 4)(x + 5) = 360$
31
Large integer help
30
Can you provide me historical examples of pure mathematics becoming “useful”?
29
Open math problems which high school students can understand
27
Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
27
Finding $\int_0^{\pi/2} \sin x\,dx$
26
Intuitive explanation of a positive-semidefinite matrix
26
How come the number $N!$ can terminate in exactly $1,2,3,4,$ or $6$ zeroes but never $5$ zeroes?
25
How to evaluate the series $1+\frac34+\frac{3\cdot5}{4\cdot8}+\frac{3\cdot5\cdot7}{4\cdot8\cdot12}+\cdots$
25
Is there a number that's right in the middle of this interval $(0, 1)$?
25
What's the formula of this sequence?
24
Why is every answer of $5^k - 2^k$ divisible by 3?
24
Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor
23
Is $\lim\limits_{k\to\infty}\sum\limits_{n=k+1}^{2k}{\frac{1}{n}} = 0$?
22
What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
21
Show $\lim\limits_{n\to\infty} n \ln\left(1-\frac{1}n\right) = -1$
21
Can you explain this card trick?
21
Does the formula $\sqrt{ 1 + 24n }$ always yield prime?
19
Value of $\sum_{n=0}^\infty (-1)^n$
18
How to do integral $\int_{-\infty}^{\infty} x^4 e^{-x^2/2}dx$
18
Find all positive integers $L$, $M$, $N$ such that $L^2 + M^2 = \sqrt{ N^2 +21}$
18
evaluate the last digit of $7^{7^{7^{7^{7}}}}$
17
An example of a norm which can't be generated by an inner product
17
$\lim_{n\to\infty} \left(\frac{1^p+2^p+3^p + \cdots + n^p}{n^p} - \frac{n}{p+1}\right)$ Evaluating this limit
16
Importance of rank of a matrix
16
Is there a formula for $\sum_{n=1}^{k} \frac1{n^3}$?
16
Show that $\sum_{n=0}^\infty \frac{\sin {nx}}{a^n} = \frac{a \sin{x}}{1 + a^{2} - 2a \cos{x}}$
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