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在数列求和的基本方法中,往往在教学中教师可能更重视倒序相加法和错位相减法,而忽视了对另外的一种重要方法裂项求和法的深入探究.先来看下面的二个例子:例1求数列{1/n(n+1)}的前n项和S n.分析在求数列的前n项和时,通常需要研究数列的通项公式.该数列的通项公式为an=1/n(n+1),容易发现,这个数列既不是等差数列又不是等比数列,那么,怎样求该数列的前n项和呢?我们知道,欲求该数列的前n项和,其关键就是要探求数列的通项公式所隐含的内在规律.由于an=1/n-1/(n+1),于是,该数列的相邻的各项之间可以消去互为相反数的项,从而
In the basic method of summation of series, teachers tend to pay more attention to the teaching of teachers more emphasis on reverse addition and dislocation subtraction method, while ignoring another important method of cracking an important method of in-depth inquiry. Two examples: Example 1 Find the first n terms and S n of the column {1 / n (n + 1)}. When evaluating the first n terms of a column, it is usually necessary to study the general formula of the series. The formula for an = 1 / n (n + 1), easy to find that this series is neither an arithmetic sequence nor an equal sequence, then how to find the first n terms and the series? We know that the desire of the series The first n terms and, the key is to explore the inherent law implied by the formula of the sequence. Because of an = 1 / n-1 / (n +1), then the sequence of adjacent items can Eliminate the opposite of each other, thus