Question

{an}中,an=(2n-1)+1/2^n,求Sn

Answer 1

解:

Sn

=a1+a2+a3+...+an

=[1+(1/2)^1]+[3+(1/2)^2]+[5+(1/2)^3]+...+[(2n-1)+(1/2)^n]

=[1+3+5+...+(2n-1)]+[(1/2)^1 + (1/2)^2 + (1/2)^3+...+(1/2)^n]

={n[1+(2n-1)]/2}+{(1/2)[1-(1/2)^n]/(1-1/2)}

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

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