1/1×4+1/4×7...1/(3n-2)×(3n+1) 1/1×3+1/3×5...1/（2n-1）×（2n+1）Sn1=1/_数学解答

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）

人气：102 ℃　时间：2019-10-26 00:15:24

解答

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+...