已知数列{an}的通项an=1/(3n-2)(3n+1),求此数列前n项和Sn

已知数列{an}的通项an=1/(3n-2)(3n+1),求此数列前n项和Sn
已知数列{an}的通项an=1/(3n-2)(3n+1),求此数列前n项和Sn

已知数列{an}的通项an=1/(3n-2)(3n+1),求此数列前n项和Sn
an=1/(3n-2)(3n+1)
=1/3[1/(3n-2)-1/(3n+1)]
a1=1/2(1-1/4)
Sn=a1+a2+...+an
=1/3[1-1/4+1/4-1/7+...+1/(3n-2)-1/(3n+1)]
=1/3[1-1/(3n+1)]
=n/(3n+1)

原式=（1/（3n-2）-1/（3n+1））/3
故Sn=（1-1/（3n+1））/3