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如果n = 1,则如果A1 = 3 / 5n1 S(n-1)= 1-(2/3)A(n-1),则求解S1 = 1-(2/3)A1= Sn-S(n-1)=-(2/3)An +(2/3)A(n-1)然后An =(2/5)* A(n-1)然后{An}是2/ 5比率,因此数字为An =(3/5)*(2/5)^(n-1),Sn = 1-(2/3)An = 1-(2/5)*(2 /5)^(n-1)= 1-(2/5)^ nAnSn = An *[1-(2/3)An]= An-(2/3)An = An-(2/3)*(3/5)*(2/5)^(2n-2)= An-(6/25)*(4/25)^(n-1),然后是A1S1 + A2S2 +。
+ AnSn =(A1 + A2 +。
+ An)-(6/25)*[1+(4/25)+。
+(4/25)^(n-1)]= Sn-(6/25)*[1-(4/25)^ n]/(1-4 / 25)= 1-(2/5)^N-2 / 7 +(2/7)*(4/25)^ n = 5 / 7-(2/5)^ n-(4/25)^ n lim(A1S1 + A2S2 +… AnSn)(n)= 5/7