an=(4n-7)/2^n
Sn=-3/2+1/2²+5/2³+9/2^4+……+(4n-11)/2^(n-1)+(4n-7)/2^n
2Sn=-3+1/2+5/2²+9/2³+13/2^4+……+(4n-7)/2^(n-1)
两式相减,得:
Sn=-3+4/2+4/2²+4/2³+4/2^4+……+4/2^(n-1)-(4n-7)/2^n
=-3+2+1+1/2+1/4+……+1/2^(n-3)-(4n-7)/2^n
=1/2+1/4+……+1/2^(n-3)-(4n-7)/2^n
=(1/2)[1-(1/2)^(n-3)]/[1-(1/2)]-(4n-7)/2^n
=1-(1/2)^(n-3)-(4n-7)/2^n
=(2^n-8)/2^n-(4n-7)/2^n
=(2^n-8-4n+7)/2^n
=(2^n-4n-1)/2^n