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---- · 由 **----** 於星期三五月 21, 2003 5:41 pm

Evaluate

infinity
SIGMA (Fn / 2^(n+1))
n=0

Where F1=F2=1
F_(n+2)=F_(n+1)+Fn

--- · 由 **---** 於星期三五月 21, 2003 8:33 pm

you can do it too! consider Bn= Fn / 2^(n+1)) , and Fn are the sum of 2 等比 series.

---- · 由 **----** 於星期三五月 21, 2003 8:45 pm

Meowth 寫到:you can do it too! consider Bn= Fn / 2^(n+1)) , and Fn are the sum of 2 等比 series.

you mean this?
Fn = 1/sqrt5[(1+sqrt5/2)]^n - 1/sqrt5[(1-sqrt5/2)]^n

Let An =Summation [(1+sqrt5/2)]^n /2^(n+1)sqrt5
= 1/2sqrt5/[1- (1+sqrt5/4)]
= 2/sqrt5(3-sqrt5)

Bn = Summation [(1-sqrt5/2)]^n/2^(n+1)sqrt5
= 1/2sqrt5/[1-(1-sqrt5/4)]
= 2/sqrt5(3+sqrt5)

Answer = sum of these two.
=2/sqrt5 (6/4)
=3/sqrt5 ?

--- · 由 **---** 於星期三五月 21, 2003 8:48 pm

Isn't it?

scsnake · 由 **scsnake** 於星期三五月 21, 2003 9:42 pm

有更簡單的...

設原式值為a
則a-a/2-a/4=F1/4+F2/8-F1/8(why? ^^)

如果Fn是F[n-1]+F[n-2]+F[n-3]+F[n-4]+F[n-5]又如何算呢？

--- · 由 **---** 於星期三五月 21, 2003 9:46 pm

How about Generating function?

scsnake · 由 **scsnake** 於星期三五月 21, 2003 9:51 pm

你無法解5次以上的方程式^^

--- · 由 **---** 於星期三五月 21, 2003 9:53 pm

OK. I'll try it.

--- · 由 **---** 於星期三五月 21, 2003 10:05 pm

fn=f[n-1]+f[n-2]+f[n-3]+f[n-4]+f[n-5]

G(x)=f0+f1*x+f2*xx+f3*x^3+....
G(x)*x=f0*x+f1*xx+f2*xxx+f3*x^4+....
G(x)*xx=f0*xx+f1*xxx+f2*xxxx+f3*x^5+....
G(x)*xxx=f0*xxx+f1*xxxx+f2*xxxxx+f3*x^6+....
G(x)*xxxx=f0*xxxx+f1*xxxxx+f2*xxxxxx+f3*x^7+....
-------------------------------------------------------------------
G(x)*(1+x+xx+xxx+xxxx)=f0+(f0+f1)x+(f0+f1+f2)xx+(f0+f1+f2+f3)xxx+(f0+f1+f2+f3+f4)xxxx+(f1+f2+f3+f4+f5)xxxxx+...
=f0+(f0+f1)x+(f0+f1+f2)xx+(f0+f1+f2+f3)xxx+f5*xxxx+f6*xxxxx+...
=f0+(f0+f1)x+(f0+f1+f2)xx+(f0+f1+f2+f3)xxx+(G(x)-f0-f1x-f2xx-f3xxx-f4xxxx)/x

so, we can get G(x)
G(1/2) is what we want.

scsnake · 由 **scsnake** 於星期三五月 21, 2003 10:10 pm

還以為看到一堆性染巴體和巴爾氏體咧～

------
最近生物讀太多...

---- · 由 **----** 於星期三五月 21, 2003 10:12 pm

can't digest. No enzyme is powerful enough to digest this

--- · 由 **---** 於星期三五月 21, 2003 10:14 pm

xxy= male or female?
xxx= male or female?

---- · 由 **----** 於星期三五月 21, 2003 10:18 pm

xx=male
xy=female, right?
I forgot la

scsnake · 由 **scsnake** 於星期三五月 21, 2003 10:23 pm

To 234fermat:如果你指的是人類的話，那就相反囉～

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我不敢在關公meow前耍大刀～

--- · 由 **---** 於星期三五月 21, 2003 10:26 pm

有y就有鳥,沒y就沒鳥. but xxy, xxx 都不孕, right? I forget the detail.

Raceleader · 由 **Raceleader** 於星期三五月 21, 2003 10:28 pm

what is 鳥?

---- · 由 **----** 於星期三五月 21, 2003 10:31 pm

Raceleader 寫到:what is 鳥?

i think it means 男性性器官

Raceleader · 由 **Raceleader** 於星期三五月 21, 2003 10:32 pm

這用鳥好像不太文雅

scsnake · 由 **scsnake** 於星期三五月 21, 2003 10:34 pm

雞(非指器官)的性染色體和性別關係就不一樣囉～

另外，果蠅的X≧2個就是♀，但♂要有Y才有生殖力

-----
又偏題了

Raceleader · 由 **Raceleader** 於星期三五月 21, 2003 10:35 pm

OK, THAT IS ALL

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