Question

求解高数大神

这一题没看懂

Answer 1

x^n
=x^(n-2).( x^2 -1) + x^(n-2)

=x^(n-2).( x^2 -1) + x^(n-4).(x^2-1) +x^(n-4)
....
...
n 是 偶数
x^n =x^(n-2).( x^2 -1) + x^(n-4).(x^2-1) +....+ (x^2-1) +1
x^n/( x^2 -1)
= x^(n-2)+x^(n-4)+....+1 + 1/(x^2-1)
= x^(n-2)+x^(n-4)+....+1 + (1/2) [ 1/(x-1) -1/(x+1) ]
n 是奇数
x^n =x^(n-2).( x^2 -1) + x^(n-4).(x^2-1) +....+ x(x^2-1) +x
x^n/(x^2-1)
=x^(n-2)+x^(n-4)+....+x + x/(x^2-1)
=x^(n-2)+x^(n-4)+....+x + (1/2) [ 1/(x-1) + 1/(x+1) ]

Answer 2

自己动手用多项式除法除一下就知道了。