Question

已知数列｛an｝是公差不为0的等差数列，a1，a2，a7成等比数列，

a3+a7=34。当an=b1/2+b2/2ˆ2+b3/2ˆ3+···

Answer 1

(1)
设{an}公差为d,d≠0
∵a2=3，a1、a3、a7成等比数列
∴{a1+d=3
①
{(a1+2d)²=a1(a1+6d)
②
②==>4a1d+4d²=6a1d
==>
a1d=2d,
∵d≠0
∴a1=2
,d=1
∴范怠顿干塥妨舵施罚渐an=n+1
(2)
bn=(n+1)/(n+2)+(n+2)/(n+1)
=[(n+2)-1]/(n+2)+[(n+1)+1]/(n+1)
=2+1/(n+1)-1/(n+2)
∴数列bn的前n项和
sn=（2+1/2-1/3+2）+(2+1/3-1/4)+........+[2+1/(n+1)-1/(n+2)]
=2n+1/2-1/(n+2)