论文部分内容阅读
在世界数学史上。对级数的讨论具有悠久的历史,古代希腊、埃及和印度都曾研究过级数。我国也从古代开始就对级数进行研究,数学家沈括、杨辉、朱世杰与李善兰等对级数的研究更是取得相当大的成就。沈括的“隙积”、朱世杰的“垛积’。都有求级数和的创造性的算法。 1989年全国高考理科数学试题第23题:是否存在常数a、b、c,使得等式1·2~2+2.3~2+…+n(n+1)~2=(n(n+1))/12(an~2+bn+c)对一切自然数n都成立?并证明你的结论.很易确定α=3、b=11、c=10,用数学归纳法证明S_n=1/12n·(n+1)(n+2)(3n+5)正确。
In the history of mathematics in the world. The discussion of the series has a long history. Ancient Greece, Egypt and India have all studied the series. China has also studied series from ancient times, and mathematicians such as Shen Kuo, Yang Hui, Zhu Shijie, and Li Shanlan have made considerable achievements in the study of the series. Shen Kuo’s “gap product” and Zhu Shijie’s “hoarding.” Both have a creative algorithm for seeking series and. In the 1989 National College Mathematics mathematics test question 23: Is there a constant a, b, c, so that equation 1· 2~2+2.3~2+...+n(n+1)~2=(n(n+1))/12(an~2+bn+c) holds for all natural numbers n and proves your conclusion It is easy to determine α=3, b=11, c=10, and use mathematical induction to prove that S_n=1/12n·(n+1)(n+2)(3n+5) is correct.