学帮网1/1×4+1/4×7...1/(3n-2)×(3n+1) 1/1×3+1/3×5...1/（2n-1）×（2n+1）Sn1=1/1×4+1/4×7...1/(3n-2)×(3n+1)Sn2=1/1×3+1/3×5...1/（2n-1）×（2n+1）
来源：学生作业学帮网 编辑：学帮网 时间：2024/05/22 21:36:35
1/1×4+1/4×7...1/(3n-2)×(3n+1) 1/1×3+1/3×5...1/（2n-1）×（2n+1）
Sn1=1/1×4+1/4×7...1/(3n-2)×(3n+1)
Sn2=1/1×3+1/3×5...1/（2n-1）×（2n+1）
1/[(3n-2)×(3n+1)]
=1/3*[1/(3n-2)-1/(3n+1)]
则Sn1=1/(1×4)+1/(4×7)...1/[(3n-2)×(3n+1)]
=1/3*[1/1-1/4+1/4-1/7+……+1/(3n-2)-1/(3n+1)]
=1/3*[1-1/(3n+1)]
=n/(3n+1)
1/[（2n-1）×（2n+1）]
=1/2*[1/(2n-1)-1/(2n+1)]
所以
Sn2=1/(1×3)+1/(3×5)...1/[（2n-1）×（2n+1）]
=1/2*[1/1-1/3+1/3-1/5+……+1/(2n-1)-1/(2n+1)]
=1/2*[1-1/(2n+1)]
=n/(2n+1)