Re: 麥克勞林及數
※ 引述《chat543 (小ㄐ)》之銘言：
: 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) .
: 我用排列組合 C 算~算到這邊就不到怎嚜求了= ="?
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
※ 編輯: mrx750926 來自: 118.160.180.199 (07/06 19:14)
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07/06 19:45, , 1F
07/06 19:45, 1F
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