{an}为无穷等比数列,公比|q|<1,且每一项与它以后的所有项的和之比2:3,求公比q
\u65e0\u7a77\u7b49\u6bd4\u6570\u5217{an}\u4e2d\uff0c\u516c\u6bd4\u4e3aq\uff0c\u4e14\u6240\u6709\u9879\u7684\u548c\u4e3a2/3\uff0c\u5219a1\u7684\u8303\u56f4\u662f________\u8be6\u7ec6\u6c42\u89e3\u8fc7\u7a0b\u5982\u4e0b
an=a1\u00d7q^(n-1)=9/8\u00d7(2/3)^(n-1)=1/3
\u6240\u4ee5 (2/3)^(n-1)=(1/3)\u00d7(8/9)
(2/3)^(n-1)=8/27
\u5f97 n-1=3
\u6240\u4ee5 n=4
an/Rn=an/[a(n+1)/(1-q)]=(1-q)/q=2/3;
解得q=3/5.
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