作者metastable (亚稳)
看板trans_math
标题期考提 数列
时间Mon Jun 24 09:41:45 2013
The Binomial Theorem implies that
(2n)! n
(1-x)^-(1/2) = 1 +Σ ------------- X
n=1 4^n *(n!)^2
(b)Estimate the error if one uses x = -1/4
and the first five non-zero terms in (a) to approximate 1/√5
<sol>
(b) (2n)! n
1/√5 =
(1/2)((1-(-1/4))^-1/2=
(1/2)Σ ------------- X
n=0 4^n *(n!)^2
Since it is an alternating series (2 points)
(2n)! n 10!
∣1/√5 - (1/2)Σ ------------- X ∣≦ ---------------
n=0 4^n *(n!)^2 2 *4^10 (5!)^2
那个1/2是怎麽出来的 还有下面那段我也看不太懂 可以解释一下吗
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.114.123.88
※ 编辑: metastable 来自: 140.114.123.88 (06/24 09:42)
1F：推 suhorng:1/√[1-(-1/4)] = 1/√(4/5) = 2/√5 118.166.44.209 06/24 10:39
2F：→ suhorng:下面那段就alternating series误差估计 118.166.44.209 06/24 10:39
3F：→ suhorng:误差不超过略去的第一项 118.166.44.209 06/24 10:40
4F：推 newversion:楼上 1/√(5/4) 才对 140.112.251.86 06/24 15:47
5F：→ suhorng:感谢楼上 118.166.44.209 06/24 18:01