无穷递缩等比数列之和
问题描述：
无穷递缩等比数列之和
1.一无穷递缩等比数列,琪第二项为-2,无穷项和4.5,求此数列的通项公式.
2.若等比数列a,-a/2,a/4,...的无穷项之和为8,求a.
3.求下列各等比数列的无穷项之和.
1.1/4,1/12,1/36...2.50,10,2.
答
a(n)=aq^(n-1),|q|1(舍去）,q=-1/3.
a=-2/q = 6.
a(n)=6(-1/3)^(n-1)=6/(-3)^(n-1),
2,
q=-1/2,
a(n)=a(-1/2)^(n-1),
8 = a/(1+1/2) = (2/3)a,a = 12.
3,
(1) a(n) = (1/4)(1/3)^(n-1),
s=(1/4)/[1-1/3]=(1/4)/(2/3) = 3/8,
(2) a(n) = 50(1/5)^(n-1),
s = 50/(1-1/5) = 50/(4/5) = 125/2