pmaths complex number

bearwing

上述proof 是否正確?
如錯, 煩請指正

[ 本帖最後由 bearwing 於 21-8-2008 00:48 編輯 ]

HKwww

sin/cos轉e function係pure math好似係OUT C架喎
呢個expression我都係係APP見過一次

[S]【YU】

呢個Euler formula係Signal Processing係成日用...
adamsteve將會係ELEC2201成日用.

adamsteve

唔係呀ma=.= 數係我最差哥科黎架 今次要多加努力啦
year2 唔可以再係咁hea gpa

Zend

我都要sit 下果個乜MATH1805 先...

你地Engine 竟然有自己的Maths course, 好唔開心[[tk_35]]

我BSc  yr 1: yr2: yr3 係1:1:1
一 仆到, 就真仆到[[tk_41]]

adamsteve

engine梗係有自己course啦
哥科叫做engineering maths喎 我地係maths+phy ge完全混合體 加少少chem咁啦

Zend

我好似無乜機會去到黃克競果邊 -.-

bearwing

浮下上水先

Let
1 + (2/3)cosx + (4/9)cos2x + ... + (2/3)^n cos nx = {a_n}
0 + (2/3)sinx + (4/9)sin2x + ... + (2/3)^n sin nx = {b_n}
1 + (2/3)e^ix + (4/9)e^2ix + ... + (2/3)^n e^nix = {e_n}

Q1. How to prove {a_n} is convergent? ( or {b_n}, as they are the same}
Q2. Shall I prove the convergence of {a_n} and {b_n} first before I separate
lim{e_n} = lim{a_n} + i lim{b_n} ?

thx very much.

[ 本帖最後由 bearwing 於 26-8-2008 23:25 編輯 ]

博士．Dota

原帖由 bearwing 於 26-8-2008 01:48 發表
浮下上水先

Let
1 + (2/3)cosx + (4/9)cos2x + ... + (2/3)^n cos nx = {a_n}
0 + (2/3)sinx + (4/9)sin2x + ... + (2/3)^n sin nx = {b_n}
1 + (2/3)e^ix + (4/9)e^2ix + ... + (2/3)^n e^nix = {e_n}

Q1 ...

Q2 我唔知，Q1 我會咁答：
{a_n} 收歛，因為...

[ 本帖最後由 博士．Dota 於 27-8-2008 16:39 編輯 ]

bearwing

原帖由 博士．Dota 於 27-8-2008 12:52 發表


Q2 我唔知，Q1 我會咁答：
{a_n} 收歛，因為...

佩服[[bao_41]]

原來條問題係limit of series, 唔係pure 野
http://en.wikipedia.org/wiki/Convergent_series

我都係唔係好明absolute convergence 個concept...

[ 本帖最後由 bearwing 於 27-8-2008 19:40 編輯 ]