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数列…(Ⅰ)称为变号数列。怎样求变号数列前n项的和?有的书上先分n为奇数和偶数两类,然后在每一类中再求数列{(-1)~(n-1)a_n}的奇数项的和与偶数项的和,最后用分段函数的形式给出数列{(-1)~(n-1)a_n}的前n项的和的公式。这种方法比较繁杂,我们试给出一种统一的方法。
The series ... (I) is called a variable number sequence. How to find the sum of the first n terms of a variable number sequence? Some books first divide n into two types, odd and even, and then find the odd entries of the sequence {(-1)~(n-1)a_n} in each class. The sum of the sums of the sums and the even-numbered terms gives the formula for the sum of the first n terms of the series {(-1)~(n-1)a_n} in the form of a piecewise function. This method is complicated and we try to give a unified method.