Question

数列题 帮下忙A1=1 A(n+1)=2An+2^n（2的N次方）求A的通向

Answer 1

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

同除以2^n

a(n+1)/2^n=2an/2^n+1

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

所以数列｛an/2^(n-1)｝为以1为公差的等差数列

a1/2^0=1

an/2^(n-1)=1+(n-1)*1=n

所以an = n2^(n-1)