Question

帮我看看这个级数题目把这个级数改写成（z-1)幂展开式z/(z^2-2z+5)

Answer 1

z/(z^2-2z+5)

=[（z-1）+1]/[4+(z-1)^2]

=（z-1）/4*[1/(1+((z-1)/2)^2]+1/4*[[1/(1+((z-1)/2)^2]]

=（z-1）/4*[1-(z-1)/2+.+(-(z-1)/2)^n+0(x)]+1/4*[1-(z-1)/2+.+(-(z-1)/2)^n+0(x）]

自己再稍微整理一下