数列1/2X5,1/5X8,1/8X11,、、、1/[(3N-1)X(3N+2)]的前N项和是

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 16:16:56

数列1/2X5,1/5X8,1/8X11,、、、1/[(3N-1)X(3N+2)]的前N项和是
数列1/2X5,1/5X8,1/8X11,、、、1/[(3N-1)X(3N+2)]的前N项和是

数列1/2X5,1/5X8,1/8X11,、、、1/[(3N-1)X(3N+2)]的前N项和是
1/2X5+1/5X8+1/8X11+...+1/[(3N-1)X(3N+2)]
=1/3(1/2-1/5+1/5-1/8+...+1/(3n-1)-1/(3n+2))
=1/3*(1/2-1/(3n+2))
=n/[2(3n+2)]

1/[(3N-1)X(3N+2)]=1/3(1/(3N-1)-1/(3N+2)]
Sn=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/2(3N+2)

已经有人回答了。