①设an是等差数列,求证:{Sn/n}是等差数列
问题描述:
①设an是等差数列,求证:{Sn/n}是等差数列
②在等差数列an中,a1=-2010,其前n项和为Sn,若S2009/2009-S2007/2007=
答
S2009/2009-S2007/2007
=[2009*(a1+a2009)/2]/2009-[2007*(a1+a007)/2]/2007
=(a1+a2009)/2-(a1+a2007)/2
=a1005-a1004
=d
=-2
所以S2009=2009*2009-2009*1004*2=2009