作者mrx750926 (Mr.X)
看板trans_math
标题Re: 麦克劳林及数
时间Sun Jul 6 19:11:48 2008
※ 引述《chat543 (小ㄐ)》之铭言：
: Let f(x)=(1+x)^1/2+(1-x)^1/2 . Find the Maclaurin series for f(x) and use
: to find (20)
: f (0) .
: 我用排列组合 C 算~算到这边就不到怎嚜求了= ="?
1/2 1/2 1/2
(1+x)^(1/2) = 1 + C x + C (x^2) + C (x^3) + .....
1 2 3
1/2 1/2 1/2
+ (1-x)^(1/2) = 1 - C x + C (x^2) - C (x^3) + .....
1 2 3
------------------------------------------------------------
1/2
1/2
= 2[ 1 + 0 + C (x^2) + 0 + ... +
C (x^20) + ... ]
2
20
(20)
f'(0)
f (0)
= 1 + ------- x + .............. +
----------(x^20)+......
1!
20!
(20)
f (0) 1/2
=> ----------- = 2 C
20! 20
(20) 1/2
=> f (0) = 2*(20!)*C
20
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◆ From: 118.160.180.199
※ 编辑: mrx750926 来自: 118.160.180.199 (07/06 19:14)
1F：推 chat543:所以C不用算出来阿= ="125.229.192.196 07/06 19:45