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泰勒 (1+x)^n0

解答

泰勒

(1 + x)^{n} 0

解答

(1 + x)^{n} 0 在中心点 0 处的泰勒级数 :

求解步骤

应用泰勒公式

= 0 + \frac{\frac{d}{d x} ( ( 1 + x ) ^{n} \cdot 0 ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 + x ) ^{n} \cdot 0 ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 + x ) ^{n} \cdot 0 ) ( 0 )}{3 !} x^{3} + \dots

求导数

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10}

整理后得

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