在数列an中,已知a1=1/3,且an=-2Sn*S(n-1),求lim[an/(Sn^2)]
问题描述:
在数列an中,已知a1=1/3,且an=-2Sn*S(n-1),求lim[an/(Sn^2)]
答
an = -2Sn.S(n-1)Sn - S(n-1) =-2Sn.S(n-1)1/Sn - 1/S(n-1) = 2{1/Sn}是等差数列, d=21/Sn -1/S1 = 2(n-1)1/Sn = 2n+1Sn = 1/(2n+1)an = Sn - S(n-1)= 1/(2n+1) -1/(2n-1) = -2/[(2n+1)(2n-1)] ...