Question

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/

Answer 1

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