微积分无穷小问题,求n=_____________
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微积分无穷小问题,求n=_____________
最后一步我不是很理解
![](http://img.wesiedu.com/upload/3/30/330e0b33a92f6debcb0fe7f465fd25e0.jpg)
最后一步我不是很理解
![](http://img.wesiedu.com/upload/3/30/330e0b33a92f6debcb0fe7f465fd25e0.jpg)
![微积分无穷小问题,求n=_____________](/uploads/image/z/17133010-34-0.jpg?t=%E5%BE%AE%E7%A7%AF%E5%88%86%E6%97%A0%E7%A9%B7%E5%B0%8F%E9%97%AE%E9%A2%98%2C%E6%B1%82n%3D_____________)
consider
Taylar expansion of ln(1+x)
x-x^2/2+x^3/3+...
3ln(1+x) = 3x - 3x^2/2 + x^3+...
consider
Taylar expansion of 1/(1+x)
x/(1+x) = 1-1/(1+x)
= -x+x^2-x^3+.
3ln(1+x) +x/(1+x)
= 2x +.
分母=n(n-1)x^(n-2)
the power of x =1
=> n-2 =1
n=3
Taylar expansion of ln(1+x)
x-x^2/2+x^3/3+...
3ln(1+x) = 3x - 3x^2/2 + x^3+...
consider
Taylar expansion of 1/(1+x)
x/(1+x) = 1-1/(1+x)
= -x+x^2-x^3+.
3ln(1+x) +x/(1+x)
= 2x +.
分母=n(n-1)x^(n-2)
the power of x =1
=> n-2 =1
n=3