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~~~~ --

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