# Quod Erat Demonstrandum

## 2015/01/09

### 推特老題

Filed under: HKALE,Pure Mathematics — johnmayhk @ 3:26 下午
Tags: ,

１１
１２１
１３３１
１４６４１

## 2014/01/01

### HT

Filed under: Additional / Applied Mathematics,Fun,HKALE — johnmayhk @ 12:27 上午
Tags: ,

(a) THT 比 TTT 先出現；
(b) TTT 比 THT 先出現。

（T = tail，H = head）

HHTHHHHTHTHHHTT… 就是 (a) 其中一種情況；
HTTHHHTTHHTTTHT… 就是 (b) 其中一種情況；

## 2012/04/03

### HKALE 2012 Pure Mathematics

Filed under: HKALE,Pure Mathematics — johnmayhk @ 8:53 下午

**********

＂We received a valid DMCA Notice (http://chillingeffects.org/dmca512/faq.cgi#QID130) for the following material found on your WordPress.com site:

https://johnmayhk.wordpress.com/2012/04/03/hkale-pure-mathematics-2012/

If you do not have the legal rights to distribute the file/content/material, you are required to delete the post(s) or content(s) and let us know when this has been done. The removal will then be verified, and the site will be returned to normal.

Republishing the content without permission of its copyright holder – or continuing to publish material that results in DMCA notices – will result in a permanent blog suspension. Publishing such material is a direct violation of our Terms of Service (http://wordpress.com/tos/), which you agreed to upon registration.

If you wish to formally challenge this DMCA notice, we will be happy to provide you with the details you need.＂

**********

## 2012/03/05

### 無聊講數：斯托爾茨定理

Filed under: HKALE,Pure Mathematics — johnmayhk @ 4:33 下午

1. 數列收斂之定義

$\displaystyle \lim_{n\rightarrow \infty}a_n=a$

$a_n$$a$ 的距離，可以「要多近，就有多近」。

## 2012/02/26

### 答網友：y=z^2

Filed under: HKALE,Pure Mathematics — johnmayhk @ 6:29 下午
Tags:

By considering

$(1+z)^8+(1-z)^8=0$

show that

$\displaystyle\sum_{k=0}^7 \tan^2\frac{(2k+1)\pi}{16}=56$

## 2012/01/07

### 某題-級數

Filed under: Fun,HKALE,Pure Mathematics — johnmayhk @ 12:04 上午

1 , 12 , 123 , 1234 , … , 12345678910 , 1234567891011 , …

1 , 21 , 321 , 4321 , … , 10987654321 , 1110987654321 , …

$1,\frac{12}{21},\frac{123}{321},\frac{1234}{4321},\dots$

## 2012/01/05

### 斐波那契數與二項係數

Filed under: HKALE,Pure Mathematics — johnmayhk @ 9:51 上午

$(a+b)^n=\displaystyle\sum_{r=0}^nC^n_ra^{(n-r)}b^{r}$

$(fg)^{(n)}=\displaystyle\sum_{r=0}^nC^n_rf^{(n-r)}g^{(r)}$

## 2012/01/04

### 某題-多項式

Filed under: HKALE,Pure Mathematics — johnmayhk @ 11:08 上午

$p(x)=p(x-1)$ for all $x \in \mathbb{R}$

## 2011/10/18

### Chain rule

Filed under: HKALE,NSS,Pure Mathematics,Teaching — johnmayhk @ 4:29 上午
Tags: ,

## 2011/10/14

### 旋轉體體積

Filed under: HKALE,NSS,Pure Mathematics — johnmayhk @ 7:47 上午

## 2011/10/10

### 錯在哪裡之 0 = 1

Filed under: HKALE,NSS,Pure Mathematics — johnmayhk @ 5:29 上午
Tags:

Old stuff…

$\int \frac{\cos \theta d\theta}{\sin \theta}$

$=\int \frac{d\sin \theta}{\sin \theta}$ (more…)

## 2011/10/04

### 純數堂無聊一記

Filed under: HKALE,Pure Mathematics — johnmayhk @ 4:23 下午

$|\int_0^x(x-t)^mf^{(m+1)}(t)dt| \le\int_0^x|(x-t)^mf^{(m+1)}(t)|dt$ ($\forall x \in \mathbb{R}$)

## 2011/09/23

### second fundamental theorem of calculus

Filed under: HKALE,Pure Mathematics,Teaching — johnmayhk @ 11:42 上午

$\frac{d}{dx}\int_a^xf(t)dt=f(x)$

（其中 $f$ 在開區間 $I$ 內連續，$a\in I$ 是常數。）

$\frac{d}{dx}\int_0^x(x-t)^2dt$ 是甚麼？ (more…)

## 2011/08/19

### 某數算題

Filed under: Additional / Applied Mathematics,HKALE,NSS,Teaching — johnmayhk @ 6:34 下午

If three tickets are chosen at random without replacement from a set of 6n tickets numbered respectively 1, 2,…, 6n, what is the probability that the sum of the numbers on the numbers on the chosen tickets is 6n?

## 2011/08/17

### 還是數算

Filed under: Additional / Applied Mathematics,HKALE,NSS,Teaching — johnmayhk @ 11:29 下午

There are 10 empty boxes. 5 balls are going to put one by one into a randomly selected box. Find the probability that two of the boxes each contains 2 balls.