a(n+1)=an+2^n
=a(n-1)+2^n+2^(n-1)
=a1+2^n+2^(n-1)+......+2^2+2^1
=a1+[2×(1-2^n)]/(1-2)
=2+2×2^n-2
=2^(n+1)
所以，an=2^n
望采纳哈！
a(n+1)-an=2^n
a2=a1+2^1
a3=a2+2^2=a1+2^1+2^2
......
an=a1+2^1+2^2+...+2^n
=2+2(1-2^n)/(1-2)
=2^(n+1)
an=(an-an-1)+(an-1-an-2)+...+(a2-a1)+a1=2^(n-1)+2^(n-2)+...+2^1+2=2^n
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