1/1×4+1/4×7...1/(3n-2)×(3n+1) 1/1×3+1/3×5...1/(2n-1)×(2n+1)

问题描述:

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+...