Question

高数题求解。·？

Answer 1

1/(x+4)=1/(5+(x-1))
=1/5 * (1/(1+(x-1)/5))
然后用一个等比级数的结论：
1/(1+q) = Σ(-q)^n，其中n从0取到∞，陪伍凯
用(x-1)/5代替上面的芦唤q，你就知道原答案是什么了橘好

Answer 2

f(x)=1/(x+4) =>f(1) = 1/5
f'(x) =-1/(x+4)^2 =>让亩f'(1)/1! = -1/25
f^(n)(x) =(-1)^n . n!/(x+4)^(n+1)
=>昌嫌f^(n)(1)/n! = (-1)^n /5^(n+1)
f(x)
=1/耐滑手(x+4)
=1/5 -(1/25)(x-1) + (1/125)(x-1)^2+...+ [(-1)^n /5^(n+1) ] (x-1)^n +....