已知数列{an},an=1/n²+2n,求sn

已知数列{an},an=1/n²+2n,求sn
已知数列{an},an=1/n²+2n,求sn

已知数列{an},an=1/n²+2n,求sn
a1=1/2(1-1/3)
a2=1/2(1/2-1/4)
a3=1/2(1/3-1/5)
an=1/2[1/n-1/(n+2)]
Sn=1/2[1-1/3+1/2-1/4+1/3-1/5+…1/(n-1)-1/(n+1)+1/n-1/(n+2)]
=1/2[1+1/2-1/(n+1)-1/(n+2)]
=(3n^2+5n)/(4n^2+12n+8)