摘要
利用微分方程求（１＋ｘ）α的幂级数展开式，可避免计算其ｎ阶麦克劳林公式的余项的极限这一繁杂的过程。
in this paper, the writer comer to the conclusion that with the differential equation to calculote the binomial expansion of poweer series of the function (1 + x)α, when α is a nonzero real number, the complex procechure can be savad to calculate the limit of the complementary terms of the n steps maclaurin formula.
关键词
幂级数
微分方程
多项式
equations (1+X)￣α=αf(x) { f(0)= 1
