来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/23 06:36:42
四.9.数列知识求助,
数列1/(2乘以5),1/(5乘以8),1/(8乘以11),……的前n项和Sn为?我知道用拆项求和法,答案是n/(6n+4),我拆不出来啊,
Sn=(1/2x5)+(1/5x8)+(1/8x11)+…+(1/(3n-1)(3n+2))
=1/3[(1/2-1/5)+(1/5-1/8)+(1/8-1/11)+…+(1/(3n-1)-1/(3n+2))]
=1/3(1/2-1/(3n+2))
=n/(6n+4)