已知数列{an}的前n项和Sn,且a1=a(a为非零常数),当n>=2时,an=2Sn^2/2已知数列{an}的前n项和Sn,且a1=a(a为非零常数),当n>=2时,an=2Sn^2/2Sn-11)求证：数列｛1/Sn｝是等差数列2)设bn=Sn/an,数列bn的前n项和为Tn.已

Question

已知数列{an}的前n项和Sn,且a1=a(a为非零常数),当n>=2时,an=2Sn^2/2
已知数列{an}的前n项和Sn,且a1=a(a为非零常数),当n>=2时,an=2Sn^2/2Sn-1
1)求证：数列｛1/Sn｝是等差数列
2)设bn=Sn/an,数列bn的前n项和为Tn.已知当且仅当n=6时,Tn有最大值,求实数a取值范围.

Answer 1

n>=2,an=Sn-Sn-1=2Sn^2/2Sn-1==>1/Sn-1/Sn-1=2==>{1/Sn}是以2为公差的等差数列Sn=a/[1+(2n-2)*a]==>bn=Sn/an=-n+2-1/(2a)==>Tn=(-1/2)*n^2+[(3a-1)/(2a)]*n==>对称轴n=(3a-1)/(2a)在区间(5.5,6.5)==>-1/8...