推 owlran:cos(x^2)展開錯了。b為什麼這樣做˙_˙? 114.42.161.111 06/25 20:10
→ wei0152019:啊啊 我打錯字了 是+-交錯才對@@ 118.169.41.133 06/25 23:51
→ owlran:分母也錯...應該是要把他收回sigma的長相 114.42.161.111 06/26 00:02
→ owlran:在判斷 114.42.161.111 06/26 00:02
７.(a) Find the Taylor expansion of cos(x^2) at x=0.
(b) Determine cos(x^2) radius of convergence.
請問(b)小題我這樣算有錯嗎?
因為沒有正確解答又覺得有點奇怪，所以請各位高手幫忙解題@@
我的算法是：
x^4 x^8 x^12
cos(x^2)= 1 +-----+-----+-----+.....
2! 4! 8!
1
---------
[2(n+1)]! (2n)!
lim ------------ = lim ------------------- = 0
n→∞ 1 n→∞ (2n+2)(2n+1)(2n)!
---------
(2n)!
=> radius of convergence = ∞
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