急求一道高数幂级数展开式的详解,

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f(x) = (x-1)*2^x = 2(x-1)*2^(x-1)
= 2(x-1)*e^[ (x-1) ln2 ]
= 2(x-1) * { 1 + (x-1)ln2 + [ (x-1)ln2]^2 / 2!+ [ (x-1)ln2]^3 / 3!+…… }
= 2(x-1) + 2(x-1)^2 ln2 + (x-1)^3 (ln2)^2 + 2(x-1)^4 (ln2)^3 / 3!+……
======以下答案可供参考======
供参考答案1:
f(x)=(x-1)(2+(2*ln2)/1!*x+(2^2*ln2)^2/2!*x^2……(2^n*ln2)^n/n!*x^n)
供参考答案2:
用泰勒公式展开