麦克劳林 ((z-2))/(z-1)

解答

麦克劳林

\frac{( z - 2 )}{z - 1}

2 + z + z^{2} + z^{3} + z^{4} + \dots

求解步骤

应用麦克劳林公式

= 2 + \frac{\frac{d}{d z} ( \frac{z - 2}{z - 1} ) ( 0 )}{1 !} z + \frac{\frac{d ^{2}}{d z ^{2}} ( \frac{z - 2}{z - 1} ) ( 0 )}{2 !} z^{2} + \frac{\frac{d ^{3}}{d z ^{3}} ( \frac{z - 2}{z - 1} ) ( 0 )}{3 !} z^{3} + \dots

求导数

= 2 + \frac{1}{1 !} z + \frac{2}{2 !} z^{2} + \frac{6}{3 !} z^{3} + \frac{24}{4 !} z^{4} + \dots

整理后得

= 2 + z + z^{2} + z^{3} + z^{4} + \dots

d er i v a t i v e y = 5 - 2 t

\int_{0}^{1} (x - 1)^{3} - (x - 1) d x

in v erse l a pl a ce \frac{1}{s \cdot ( s ^{2} + \frac{9}{2} s + 15 )}

\int 2 - 1 (e - x + 2) d x

d er i v a t i v e f (x) = 3 + 2 x^{3}