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数列an前n项和为S,且an=Sn乘以Sn-1,a1=2/9,求a10
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数列an前n项和为S,且an=Sn乘以Sn-1,a1=2/9,求a10
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答案和解析
an=Sn-Sn-1=Sn*Sn-1
1/Sn-1-1/Sn=1
1/Sn-1/Sn-1=-1
数列{1/Sn}是等差数列,公差为-1
1/S1=1/a1=9/2
1/Sn=9/2+(n-1)(-1)=11/2-n=(11-2n)/2
Sn=2/(11-2n)
a10=S10-S9=2/(11-20)-2/(11-18)=-2/9+2/7=4/63
1/Sn-1-1/Sn=1
1/Sn-1/Sn-1=-1
数列{1/Sn}是等差数列,公差为-1
1/S1=1/a1=9/2
1/Sn=9/2+(n-1)(-1)=11/2-n=(11-2n)/2
Sn=2/(11-2n)
a10=S10-S9=2/(11-20)-2/(11-18)=-2/9+2/7=4/63
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