例说n项和数列极限的几种求法

Several Explorations in Resolving Limit of Number Sequence of the Sum of n Terms by Examples

有限个数列和的极限一般可用"数列和的极限等于数列极限的和"的运算法则来计算,而对于n项和数列的极限不能采用和的运算法则.针对此问题,文中利用迫敛性、定积分、幂级数和函数性质以及Fourier级数和函数得到了求此类极限的方法.

To calculate the limit of the sum of limited sequence always uses the rule ＇ the limit of the sum equals the sum of the limit＇ , but this rule cannot resolve the limit of the number sequence of the sum of n terms. Given several methods using squeeze theorem, definite integral, properties of sum function of power series and the sum function of Fourier series to resolve such limit.