Question

数列{an}中,满足下列条件,求通项an

Answer 1

a(n)=a(n-1)+2^(n-1)

a(n-1)=a(n-2)+2^(n-2)

……

a2=a1+2

累加

a(n)=a1+2+2^2+2^3+……+2^(n-1)

=1+2+2^2+2^3+……+2^(n-1)

=2^n-1