导数作为研究函数问题的新工具,在研究函数的单调性、最值等问题时比用初等数学的方法要方便、简捷得多。对于某些数学问题,若能恰当使用导数的方法,可以使问题得到很大的简化。应用一:数列求和例1,求数列1,2x,3x~2…,nx~(n-1)的前n项和(x≠0).解:当x≠1且x≠O时,有1+x+x~2+…+x~n=1-x/1-x~(n+1)。 Derivatives as a new tool to study the function of the problem, in the study of monotonicity, the most value and other issues than the elementary mathematics method to facilitate, much simpler. For some mathematical problems, the proper use of derivatives can make the problem greatly simplified. Application 1: Sequence Summation Example 1. Find the first n terms and (x ≠ 0) of the sequence of numbers 1,2x, 3x ~ 2 ..., nx ~ (n-1) Solution: When x ≠ 1 and x ≠ O, There are 1 + x + x ~ 2 + ... + x ~ n = 1-x / 1-x ~ (n + 1).