就是换元,令 u = x ,
e^u = 1+u + u /2! + u /3! + ...... + u^n /n! + o(x^n)
再代入 u = x , 这个是利用间接法把函数展成Maclaurin公式。
更简单的, 1/(1-x) = 1+ x + x + x + ,,,,,, + x^n + o(x^n)
1/(1-x ) = 1 + x + x( ) + ...... + x^(2n) + o(x^2n)
若令f(x) = e^(x ), f(0) = 1,
f'(x) = 2x * e^(x ), f'(0) = 0,
f''(x) = (2+4x ) * e^(x ), f''(0) = 2
f'''(x) = (12x + 8x ) * e^(x ), f'''(0) = 0
f''''(0) = 12 ......