# 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。

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

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## 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
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## 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.