关键不在于分式,而在于求和的变化,特别是指标的变化.
1/(z-2)·∑{0 ≤ n} (-1)^n·(z-2)^n
= ∑{0 ≤ n} (-1)^n·(z-2)^(n-1)
= 1/(z-2)+∑{1 ≤ n} (-1)^n·(z-2)^(n-1)
= 1/(z-2)+∑{0 ≤ n} (-1)^(n+1)·(z-2)^n
= 1/(z-2)-∑{0 ≤ n} (-1)^n·(z-2)^n.
(2/z-5)·∑{0 ≤ n} z^n
= 2/z·∑{0 ≤ n} z^n-5·∑{0 ≤ n} z^n
= 2·∑{0 ≤ n} z^(n-1)-5·∑{0 ≤ n} z^n
= 2/z+2·∑{1 ≤ n} z^(n-1)-5·∑{0 ≤ n} z^n
= 2/z+2·∑{0 ≤ n} z^n-5·∑{0 ≤ n} z^n
= 2/z-3·∑{0 ≤ n} z^n.