函数f（x）=xln（1+x）带皮亚诺型余项的麦克劳林公式为x2−x32+x43−…+(−1)n−2n−1xn+o(xn)x2−x32+x43−…+(−1)n−2n−1xn+o(xn)．

Question

函数f（x）=xln（1+x）带皮亚诺型余项的麦克劳林公式为

x2−(x3)/(2)+(x4)/(3)−…+((−1)n−2)/(n−1)xn+o(xn)

x2−(x3)/(2)+(x4)/(3)−…+((−1)n−2)/(n−1)xn+o(xn)

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Answer 1

因为ln（1+x）=x-(x2)/(2)+…+((−1)n−1xn)/(n)+o（xⁿ），
所以f（x）=xln（1+x）
=x(x−(x2)/(2)+…+((−1)n−1xn)/(n)+o(xn))
=x2−(x3)/(2)+(x4)/(3)−…+((−1)n−2)/(n−1)xn+o(xn)．
故答案为：x2−(x3)/(2)+(x4)/(3)−…+((−1)n−2)/(n−1)xn+o(xn)．