黃金比某級數

早前見某個和黃金比（Golden ratio）有關的級數（series）：

其中

乃黃金比也。

高中同學當然可以等比級數和（sum of an infinite geometric series）秒之，這裡介紹一個所謂無言證明。

如果 是黃金比，即以下長方形

sum of 1/k^2 from 1 to infinity

非正式地所謂證明 。
…………………………………………….

首先要知，下式的根之總和（sum of roots）

………. (*)

是 。

Say something about series in Applied Mathematics (II)

Here is just a typical question in AL Applied Mathematics (II).

For natural numbers ().

Let , evaluate .

Just a question of applied math. from a F.7 boy

Just discuss an easy AL Applied Mathematics (II) Question with students.

Let be twice differentiable functions such that .

(a) Let , where . Show that .

(b) Using (a), or otherwise, find Taylor’s expansion of the function about , up to the term in .