已知公差不为0的等差数列an首项a1为a,前n项和为Sn,且1/a1,1/a2,1/a3为等比数列,求an及Sn
问题描述：
已知公差不为0的等差数列an首项a1为a,前n项和为Sn,且1/a1,1/a2,1/a3为等比数列,求an及Sn
答
1/a 1/(a+2d)=1/(a+d)^2
a(a+2d)=(a+d)^2
a^2+2ad=a^2+2ad+d^2
d^2=0
d=0
哪儿写错了吧?是1/a1,1/a2,1/a4成等比数列a2^2=a1a4(a1+d)^2=a1(a1+3d)a1^2+2a1d+d^2=a1^2+3a1da1d=d^2d=a1=aan=a+(n-1)a=na