Power Series
3 3
Let f(x) = ------- and g(x) = ---------
3-x 3-x^2
a.Find a power series,centered at 0,for f(x).
b.For what values of x does the series found in part a converge?
c.Use the series found in part a to determine a power series for g(x).
d.For what values of x does the series found in part c converge?
(a) 我算出來是
3 1 ∞ x^n
f(x) = ------------ = ----------- = Σ --------
3(1 - 1/x) 1 - 1/x n = 0 3^n
(b) 我不太懂他的意思 他是要求收斂半徑嗎?
哪位大大可以告訴我提議是什麼 解法怎麼做~~
(c) 我是 Let y = x^2
3 1
=> g(y) = ---------- = ----------
3(1 - y) 1 - y
1 ∞ x^2n
=> g(x) = ----------- = Σ ---------
1 - x^2 n = 0 3^n
這樣算有錯嗎?
(d) 就同(b) 不太了題意
希望有人能替我解惑~~~~
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.128.194.71
討論串 (同標題文章)
完整討論串 (本文為第 1 之 2 篇)：