数列的问题已知数列{an}满足对任意的正整数n,都有a1+a2+
已知数列{an}满足对任意的正整数n,都有a1+a2+a3......+an=2^(n-1) 则 a1^2+a2^2+a3^2.....+an^2=
A1+A2+A3......+An=2^(n-1) ==> A1+A2+A3......+A(n-1)=2^(n-2) ==> An = 2^(n-1) - 2^(n-2) = 2^(n-2), A1 = 1 ==> a1^2+a2^2+a3^2.....+an^2 = A1 + (a2^2+a3^2.....+an^2) = [2 + 4^(n-1)]/3