已知等差数列｛an｝,a1=2,s2010/2010-s2008/2008=2,求{1/sn}的前n项和?

已知等差数列｛an｝,a1=2,s2010/2010-s2008/2008=2,求{1/sn}的前n项和?
已知等差数列｛an｝,a1=2,s2010/2010-s2008/2008=2,求{1/sn}的前n项和?

已知等差数列｛an｝,a1=2,s2010/2010-s2008/2008=2,求{1/sn}的前n项和?
设公差为d
s2010=2X2010+2010X2010d/2
s2008=2X2008+2008X2008d/2
代入已知等式,求得d=2,则：an=2n
s1=2
s2=6
s3=12
.
sn=n(n+1)
{1/sn}的前N项和=1/2+1/6+1/12+.+1/[n(n+1)]