等比数列an的前n项和为Sn,若S10∕S5=31∕32,且a1=-1,求limSn
人气：438 ℃ 时间：2020-04-23 17:48:58
解答
设公比为a
S5=a1+a2+a3+a4+a5
S10-S5=a6+a7+a8+a9+a10=(a1+a2+a3+a4+a5)*(a^5)
所以(S10-S5)/S5=a^5=31/32-1= -1/32
所以a= -1/2
limSn=a1/(1-a)= -1/(3/2)= -2/3
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