已知数列an中 a1=-2且an+1=sn(n+1为下标),求an,sn
问题描述:
已知数列an中 a1=-2且an+1=sn(n+1为下标),求an,sn
答
已知 a_(n+1)=S_n 得 a_n=S_(n-1)(n>1)两式相减 a_(n+1) - a_n = S_n - S_(n-1) = a_n (n>1)得 a_(n+1) = 2a_n (n>1)因为 a_2 = S_1 = a_1 = -2所以 a_n=-2^(n-1) (n>1,a1=-2);S_n = a_(n+1) =-2^n...