Question

数列{an}中,任意自然数n,a1+a2+a3=...+an=2的n次方-1则a1方+a2方+.an方等于

Answer 1

an=Sn-S(n-1)

=2^n-1-[2^(n-1)-1]

=2^(n-1)

an^2=4^(n-1)

a1^2=1

a1^2+a2^2+...+an^2=(1-4^n)/(1-4)=(4^n-1)/3