数列an前n项和为S,且an=Sn乘以Sn-1,a1=2/9,求a10_数学解答

数列an前n项和为S,且an=Sn乘以Sn-1,a1=2/9,求a10

人气：297 ℃　时间：2020-04-11 01:03:16

解答

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