Question

求和.Sn=1*2+4*2平方+7*2的3次方+…+(3n-2)*2的n次方

Answer 1

Sn=1*2+4*2平方+7*2的3次方+…+(3n-2)*2的n次方

(1/2)Sn=1+4*2+7*2^2+.+(3n-2)*2^(n-1)

(1/2)Sn-Sn=1+3*2+3*2^2+...+3*2^(n-1)-(3n-2)*3^n

-(1/2)Sn=1+3*2*[2^(n-1)-1]/(2-1)-(3n-2)*2^n

=1+3*2^n-6-(3n-2)*2^n

=-5-(3n-5)*2^n

所以Sn=(3n-5)*2^(n+1)+10