partial-fraction expansion

例句：

1. 1.In the partial-fraction expansion of the series, we can see that the sum of the first n terms is given by the formula for a geometric series.
   在数列的部分分式展开中，我们可以看到第n项的和由几何级数公式给出。
2. 2. The partial-fraction expansion of the function f(x) = x^3 - 4x^2 + 3x - 1 is given by the series (1/2)^3 + (1/3)^3 + (1/4)^3 + ... + (1/n)^3.
   函数f(x) = x^3 - 4x^2 + 3x - 1的部分分式展开为这个级数：1/2^3 + 1/3^3 + 1/4^3 + ... + 1/n^3。
3. 3.In this example, the partial-fraction expansion of the function f(x) = x^3 - 4x^2 + 3x - 1 is used to find the roots of the cubic equation.
   在这个例子中，我们使用函数f(x) = x^3 - 4x^2 + 3x - 1的部分分式展开来找到三次方程的根。