嚙瘩嚙踝蕭(嚙複橘蕭)
2011-9-6 17:34
Justice
嚙瘩嚙踝蕭(嚙複橘蕭)
[size=1] 2 n 2[/size]
嚙緩嚙踝蕭(1-2x) (1+x) =a+bx+cx +... 嚙璀嚙賭中a嚙畿b嚙瞎c嚙踝蕭嚙窯嚙複。
a,嚙調以n嚙踝蕭嚙踝蕭b嚙瞎c嚙瘠
[size=1] 2[/size]
b,嚙磐x 嚙踝蕭嚙磐嚙複是-5嚙璀嚙瘩n嚙踝蕭嚙褓。
2011-9-6 18:12
UniCorn
(1-2x)^2 (1+x)^n =(1 - 4x + 4x^2)(1 + nx + n(n-1)x^2 / 2 + ......)
= 1 + nx + n(n-1)x^2 / 2 - 4x -4nx^2 + 4x^2 +......
= 1 + (n-4)x + (n(n-1)/2 - 4n + 4)x^2 + ......
2011-9-6 18:25
kimwong3252000
[img]http://i.imgur.com/WnTJS.jpg[/img]
2011-9-6 18:37
UniCorn
嚙稷嚙稻 #3 kimwong3252000 嚙踝蕭嚙踝蕭嚙締
嚙諉主嚙踝蕭嚙踝蕭嚙瘩嚙篌嚙踝蕭嚙線嚙瞌嚙諸了 nCr = n!/(r!(n-r)!)
2011-9-6 18:39
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]UniCorn[/i] 嚙踝蕭 2011-9-6 18:37 嚙緻嚙踝蕭
嚙諉主嚙踝蕭嚙踝蕭嚙瘩嚙篌嚙踝蕭嚙線嚙瞌嚙諸了 nCr = n!/(r!(n-r)!) [/quote]
嚙誹只嚙磐嚙瞌嚙踝蕭nC2- -
嚙稽嚙踝蕭嚙磐F.4嚙磕嚙褒湛蕭嚙請而家嚙踝蕭嚙踝蕭嚙磐嚙豎記嚙緻
2011-9-6 18:43
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-6 06:39 PM 嚙緻嚙踝蕭
嚙誹只嚙磐嚙瞌嚙踝蕭nC2- -
嚙稽嚙踝蕭嚙磐F.4嚙磕嚙褒湛蕭嚙請而家嚙踝蕭嚙踝蕭嚙磐嚙豎記嚙緻 [/quote]
嚙踝蕭嚙磐嚙瞌 formula 嘅嚙踝蕭 =__=
嚙誹喉蕭嚙磐F.4嚙磕嚙褒湛蕭嚙踝蕭~~
2011-9-6 18:47
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]UniCorn[/i] 嚙踝蕭 2011-9-6 18:43 嚙緻嚙踝蕭
嚙踝蕭嚙磐嚙瞌 formula 嘅嚙踝蕭 =__=
嚙誹喉蕭嚙磐F.4嚙磕嚙褒湛蕭嚙踝蕭~~ [/quote]
嚙複鳴蕭formula?
嚙窯嚙踝蕭嚙誹只嚙磐嚙瞌
nC1=nx
nC2=n(n-1)x^2
2011-9-6 18:55
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-6 06:47 PM 嚙緻嚙踝蕭
嚙複鳴蕭formula?
嚙窯嚙踝蕭嚙誹只嚙磐嚙瞌
nC1=nx
nC2=n(n-1)x^2 [/quote]
nCr = n!/(r!(n-r)!)
(nCr 嚙磅嚙踝蕭x嚙踝蕭...btw,nC2 嚙罵嚙瘤0.5)
nC0 = n!/(0!(n-0)!) = 1
nC1 = n!/(1!(n-1)!) = (n(n-1)!)/(1!(n-1)!) = n
nC2 = n!/(2!(n-2)!) = (n(n-1)(n-2)!)/(2!(n-2)!) = n(n-1)/2
nC3 = n!/(3!(n-3)!) = (n(n-1)(n-2)(n-3)!)/(3!(n-3)!) = n(n-1)(n-2)/6
etc.
2011-9-6 18:58
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]UniCorn[/i] 嚙踝蕭 2011-9-6 18:55 嚙緻嚙踝蕭
nCr = n!/(r!(n-r)!)
(nCr 嚙磅嚙踝蕭x嚙踝蕭...btw,nC2 嚙罵嚙瘤0.5)
nC0 = n!/(0!(n-0)!) = 1
nC1 = n!/(1!(n-1)!) = (n(n-1)!)/(1!(n-1)!) = n
nC2 = n!/(2!(n-2)!) = (n(n-1)(n-2)!)/(2!(n-2)!) = n(n-1)/2
nC3 ... [/quote]
嚙課試最多嚙豎剁蕭nC3, 嚙踝蕭嚙諉哨蕭嚙罵嚙豎剁蕭nC4嚙踝蕭-.-
2011-9-6 19:00
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-6 06:58 PM 嚙緻嚙踝蕭
嚙課試最多嚙豎剁蕭nC3, 嚙踝蕭嚙諉哨蕭嚙罵嚙豎剁蕭nC4嚙踝蕭-.- [/quote]
嚙誹以嚙箴嚙調過嚙篁嚙踝蕭 nC12(嚙踝蕭
2011-9-6 19:02
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]UniCorn[/i] 嚙踝蕭 2011-9-6 19:00 嚙緻嚙踝蕭
嚙誹以嚙箴嚙調過嚙篁嚙踝蕭 nC12(嚙踝蕭 [/quote]
nC12 嚙諄剁蕭L嚙踝蕭k嚙稼嚙踝蕭, 嚙踝蕭嚙緬嚙磐嚙豎寫嚙踝蕭- -
2011-9-6 19:14
Justice
thx
嚙踝蕭:
Q嚙瘦嚙踝蕭x嚙踝蕭嚙褕橘蕭嚙褒，嚙箠嚙罷嚙磊嚙瘠嚙磊嚙踝蕭嚙踝蕭x^3嚙踝蕭嚙瘠
1 [size=1]2x -2x[/size]
嚙瑾(e +e )
2
ps嚙瘦e嚙瞌嚙踝蕭2.718281828
[[i] 嚙踝蕭嚙踝蕭嚙諒恬蕭嚙� Justice 嚙踝蕭 2011-9-6 19:20 嚙編嚙踝蕭 [/i]]
2011-9-6 19:16
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]Justice[/i] 嚙踝蕭 2011-9-6 19:14 嚙緻嚙踝蕭
thx
嚙踝蕭:
Q嚙瘦嚙踝蕭x嚙踝蕭嚙褕橘蕭嚙褒，嚙箠嚙罷嚙磊嚙瘠嚙磊嚙踝蕭嚙踝蕭x^3嚙踝蕭嚙瘠
1 2x -2x
嚙瑾(e +e )
2
ps嚙瘦e嚙瞌嚙踝蕭2.718281828 [/quote]
e嚙誹好嚙緲, 嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭-.-
2011-9-6 19:47
Justice
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-6 19:16 嚙緻嚙踝蕭
e嚙誹好嚙緲, 嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭-.- [/quote]
嚙踝蕭嚙瞇嚙碾嚙罵嚙瘤
2011-9-6 20:59
issac999
嚙緻嚙瞌嚙複鳴蕭伬啎~嚙請迎蕭=.=?
嚙緯嚙踝蕭..........
嚙豌鳴蕭嚙踝蕭嚙複鳴蕭嚙線pload嚙瞇嚙豌塚蕭嚙踝蕭= =
help...
2011-9-6 21:01
Amuro
嚙稷嚙稻 #15 issac999 嚙踝蕭嚙踝蕭嚙締
嚙踝蕭嚙罵 嚙複學抬蕭嚙踝蕭1嚙緩嚙踝蕭嚙踝蕭2
2011-9-6 21:06
issac999
嚙稷嚙稻 #16 Amuro 嚙踝蕭嚙踝蕭嚙締
嚙踝蕭嚙褒得嚙緣嚙稿嚙豎大.............
2011-9-6 21:11
akji47
[quote]嚙趣帖嚙踝蕭 [i]issac999[/i] 嚙踝蕭 2011-9-6 21:06 嚙緻嚙踝蕭
嚙踝蕭嚙褒得嚙緣嚙稿嚙豎大............. [/quote]
M1 M2 嚙踝蕭嚙緯嚙踝蕭bio嚙踝蕭
2011-9-6 21:49
issac999
嚙稷嚙稻 #18 akji47 嚙踝蕭嚙踝蕭嚙締
嚙誹仲未教剁蕭O嚙踝蕭-.-
嚙踝蕭嚙踝蕭
2011-9-6 22:45
0123
formula嚙磐M2嚙踝蕭嚙請架???
2011-9-6 23:14
Freedom_X10a
[youtube]sa1625eoJcM[/youtube]
2011-9-7 00:03
嚙踝蕭嚙瑾嚙踝蕭
嚙璀嚙踝蕭嚙緹嚙論堆蕭Binomial Therom嚙褕只嚙緯嚙瞌嚙踝蕭General Term嚙瞇嚙緯
嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾[size=1]n[/size]
The General Term of the expansion of (x+y)
嚙瑾嚙瑾嚙瑾 [size=1]n-r[/size] [size=1]r[/size]
=nCr (x) (y)
e嚙稽嚙瞌嚙璀嚙瞌嚙踝蕭[img]http://upload.wikimedia.org/math/0/b/c/0bc08045195dc823c22d1fa283cb0759.png[/img]
嚙緲嚙璀嚙踝蕭嚙褕小嚙賠一嚙瘢嚙瞇嚙磅嚙踝蕭嚙瘩嚙瘤
2011-9-7 00:14
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-6 07:02 PM 嚙緻嚙踝蕭
nC12 嚙諄剁蕭L嚙踝蕭k嚙稼嚙踝蕭, 嚙踝蕭嚙緬嚙磐嚙豎寫嚙踝蕭- - [/quote]
嚙璀嚙踝蕭嚙踝蕭L嚙踝蕭k嚙踝蕭 = =
[quote]嚙趣帖嚙踝蕭 [i]Freedom_X10a[/i] 嚙踝蕭 2011-9-6 11:14 PM 嚙緻嚙踝蕭
sa1625eoJcM [/quote]
嚙線嚙篁嚙踝蕭...
嚙誹瘀蕭嚙褕常嚙窯嚙箭嚙瞋1嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭h嚙瘡...
[[i] 嚙踝蕭嚙踝蕭嚙諒恬蕭嚙� UniCorn 嚙踝蕭 2011-9-7 07:37 嚙編嚙踝蕭 [/i]]
2011-9-7 19:42
Justice
[quote]嚙趣帖嚙踝蕭 [i]嚙踝蕭嚙瑾嚙踝蕭[/i] 嚙踝蕭 2011-9-7 00:03 嚙緻嚙踝蕭
嚙璀嚙踝蕭嚙緹嚙論堆蕭Binomial Therom嚙褕只嚙緯嚙瞌嚙踝蕭General Term嚙瞇嚙緯
嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾嚙瑾n
The General Term of the expansion of (x+y)
嚙瑾嚙瑾嚙瑾 n-r r
=nCr (x) (y)
e嚙稽嚙瞌嚙璀嚙瞌[img]http://upload.wikimedia.org/math/0/b/c/0bc08045195dc823c22d1fa283cb0759.png[/img][/quote]
Q嚙瘦嚙踝蕭x嚙踝蕭嚙褕橘蕭嚙褒，嚙箠嚙罷嚙磊嚙瘠嚙磊嚙踝蕭嚙踝蕭x^3嚙踝蕭嚙瘠
1 [size=1]2x -2x[/size]
嚙瑾(e +e )
2
==================================
嚙緻嚙瘩嚙誹歹蕭嚙踝蕭嚙緬嚙踝蕭J嚙踝蕭
[[i] 嚙踝蕭嚙踝蕭嚙諒恬蕭嚙� Justice 嚙踝蕭 2011-9-7 19:44 嚙編嚙踝蕭 [/i]]
2011-9-7 19:50
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]Justice[/i] 嚙踝蕭 2011-9-7 19:42 嚙緻嚙踝蕭
Q嚙瘦嚙踝蕭x嚙踝蕭嚙褕橘蕭嚙褒，嚙箠嚙罷嚙磊嚙瘠嚙磊嚙踝蕭嚙踝蕭x^3嚙踝蕭嚙瘠
1 2x -2x
嚙瑾(e +e )
2
==================================
嚙緻嚙瘩嚙誹歹蕭嚙踝蕭嚙緬嚙踝蕭J嚙踝蕭 [/quote]
嚙踝蕭嚙盤嚙踝蕭嚙踝蕭?
2011-9-7 20:15
Justice
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-7 19:50 嚙緻嚙踝蕭
嚙踝蕭嚙盤嚙踝蕭嚙踝蕭? [/quote]
[size=1] 2[/size]
1+2x+...
2011-9-7 20:44
kimwong3252000
[img]http://i.imgur.com/b4h6e.jpg[/img]
2011-9-7 20:46
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-7 20:44 嚙緻嚙踝蕭
[img]http://i.imgur.com/b4h6e.jpg[/img] [/quote]
嚙綞嚙踝蕭嚙瞌嚙緻add嚙踝蕭x^3 tim
嚙踝蕭梜嚙踝蕭Ycancel嚙踝蕭, 嚙璀嚙踝蕭嚙踝蕭嚙踝蕭嚙諸架嚙踝蕭
[color=White](嚙踝蕭嚙踝蕭? 嚙踝蕭嚙踝蕭? x^3嚙踝蕭term嚙磐 (4/3)x^3)[/color]
2011-9-7 20:50
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]Justice[/i] 嚙踝蕭 2011-9-7 07:42 PM 嚙緻嚙踝蕭
Q嚙瘦嚙踝蕭x嚙踝蕭嚙褕橘蕭嚙褒，嚙箠嚙罷嚙磊嚙瘠嚙磊嚙踝蕭嚙踝蕭x^3嚙踝蕭嚙瘠
1 2x -2x
嚙瑾(e +e )
2
==================================
嚙緻嚙瘩嚙誹歹蕭嚙踝蕭嚙緬嚙踝蕭J嚙踝蕭 [/quote]
[img]http://upload.wikimedia.org/math/0/b/c/0bc08045195dc823c22d1fa283cb0759.png[/img]
put x =2x
e^2x = 1 + 2x + 4x^2 / 2+.....
put x =-2x
e^-2x = 1 - 2x + 4x^2 / 2+.....
e^2x + e^-2x = 1 + 2x + 4x^2 / 2 + 1 - 2x + 4x^2 / 2 +......
= 2 + 4x^2 +......
(e^2x + e^-2x )/2 = (2 + 4x^2)/2 +......
= 1 + 2x^2 +......
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-7 08:44 PM 嚙緻嚙踝蕭
[img]http://i.imgur.com/b4h6e.jpg[/img] [/quote]
嚙踝蕭A嚙誰過嚙踝蕭...
嚙盤scanner嚙線嚙磐嚙蝓瘀蕭...
[[i] 嚙踝蕭嚙踝蕭嚙諒恬蕭嚙� UniCorn 嚙踝蕭 2011-9-7 20:53 嚙編嚙踝蕭 [/i]]
2011-9-7 20:51
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]UniCorn[/i] 嚙踝蕭 2011-9-7 20:50 嚙緻嚙踝蕭
[img]http://upload.wikimedia.org/math/0/b/c/0bc08045195dc823c22d1fa283cb0759.png[/img]
put x =2x
e^2x = 1 + 2x + 4x^2 / 2+.....
put x =-2x
e^-2x = 1 - 2x + 4x^2 / 2+.....
e^2x + e^-2x = 1 + 2 ... [/quote]
嚙璀嚙瞑嚙誹一嚙誼無嚙緘嚙踝蕭x^3
嚙踝蕭嚙瞎嚙磐cancel嚙踝蕭嚙篌, 嚙踝蕭嚙磐嚙踝蕭step嚙緯show嚙瘢
2011-9-7 21:00
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-7 08:51 PM 嚙緻嚙踝蕭
嚙璀嚙瞑嚙誹一嚙誼無嚙緘嚙踝蕭x^3
嚙踝蕭嚙瞎嚙磐cancel嚙踝蕭嚙篌, 嚙踝蕭嚙磐嚙踝蕭step嚙緯show嚙瘢 [/quote]
嚙盤嚙踝蕭嚙瘤~
2011-9-7 21:01
Justice
thx!!!嚙瞑嚙踝蕭
1 [size=1]2x -2x n[/size]
嚙踝蕭嚙誶以嚙踝蕭嚙踝蕭@(e +e )嚙豌佗蕭e 嚙踝蕭嚙課樣。
2
2011-9-7 21:02
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]Justice[/i] 嚙踝蕭 2011-9-7 21:01 嚙緻嚙踝蕭
thx!!!嚙瞑嚙踝蕭
1 2x -2x n
嚙踝蕭嚙誶以嚙踝蕭嚙踝蕭@(e +e )嚙豌佗蕭e 嚙踝蕭嚙課樣。
2 [/quote]
嚙誹歹蕭嚙箴嚙瘡嚙踝蕭嚙緯嚙踝蕭limit嚙諉堆蕭
嚙瘢嚙踝蕭嚙踝蕭茷Y嚙踝蕭嚙羯嚙皚
2011-9-7 21:38
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-7 09:02 PM 嚙緻嚙踝蕭
嚙誹歹蕭嚙箴嚙瘡嚙踝蕭嚙緯嚙踝蕭limit嚙諉堆蕭
嚙瘢嚙踝蕭嚙踝蕭茷Y嚙踝蕭嚙羯嚙皚 [/quote]
[IMG]http://i1218.photobucket.com/albums/dd404/whyeung/SMP/limit.png[/IMG]
wwwww
2011-9-7 21:41
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]UniCorn[/i] 嚙踝蕭 2011-9-7 21:38 嚙緻嚙踝蕭
[img]http://i1218.photobucket.com/albums/dd404/whyeung/SMP/limit.png[/img]
wwwww [/quote]
嚙踝蕭嚙線嚙磐嚙箠嚙瘡嚙踝蕭limit嚙踝蕭- -
嚙踝蕭limit嚙緯嚙緣
2011-9-7 21:43
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]kimwong3252000[/i] 嚙踝蕭 2011-9-7 09:41 PM 嚙緻嚙踝蕭
嚙踝蕭嚙線嚙磐嚙箠嚙瘡嚙踝蕭limit嚙踝蕭- -
嚙踝蕭limit嚙緯嚙緣 [/quote]
嚙踝蕭嚙磐嚙誹歹蕭h嚙稼嚙踝蕭limit嚙踝蕭嚙篁 wwwww
2011-9-11 22:25
akji47
[quote]嚙趣帖嚙踝蕭 [i]UniCorn[/i] 嚙踝蕭 2011-9-7 21:43 嚙緻嚙踝蕭
嚙踝蕭嚙磐嚙誹歹蕭h嚙稼嚙踝蕭limit嚙踝蕭嚙篁 wwwww [/quote]
嚙踝蕭嚙踝蕭~~
嚙豌鳴蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙罷嚙締M2嚙踝蕭嚙誹們教哨蕭嚙請得嚙緹嚙踝蕭嚙踝蕭嚙踝蕭嚙瘩~~
2011-9-11 22:27
kimwong3252000
[quote]嚙趣帖嚙踝蕭 [i]akji47[/i] 嚙踝蕭 2011-9-11 22:25 嚙緻嚙踝蕭
嚙踝蕭嚙踝蕭~~
嚙豌鳴蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙罷嚙締M2嚙踝蕭嚙誹們教哨蕭嚙請得嚙緹嚙踝蕭嚙踝蕭嚙踝蕭嚙瘩~~ [/quote]
嚙請一嚙箭XD
2011-9-11 22:30
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]akji47[/i] 嚙踝蕭 2011-9-11 10:25 PM 嚙緻嚙踝蕭
嚙踝蕭嚙踝蕭~~
嚙豌鳴蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙罷嚙締M2嚙踝蕭嚙誹們教哨蕭嚙請得嚙緹嚙踝蕭嚙踝蕭嚙踝蕭嚙瘩~~ [/quote]
嚙踝蕭訇o嚙緹~
Pure Maths 嚙踝蕭嚙線嚙磐嚙踝蕭1嚙羯嚙箭嚙請哂...
嚙緲嚙諸方面嚙瞇嚙瞌嚙緣嚙瑾嚙諉堆蕭嚙瘩嚙瘤
2011-9-11 22:32
akji47
[quote]嚙趣帖嚙踝蕭 [i]UniCorn[/i] 嚙踝蕭 2011-9-11 22:30 嚙緻嚙踝蕭
嚙踝蕭訇o嚙緹~
Pure Maths 嚙踝蕭嚙線嚙磐嚙踝蕭1嚙羯嚙箭嚙請哂...
嚙緲嚙諸方面嚙瞇嚙瞌嚙緣嚙瑾嚙諉堆蕭嚙瘩嚙瘤 [/quote]
嚙盤嚙稿嚙踝蕭(嚙緬)
嚙請改蕭嚙緻嚙踝蕭1嚙諉歹蕭N嚙踝蕭DSE(嚙緬
睇嚙諉我要嚙誼吻嚙篌嚙窮嚙瘤嚙皺嚙皺