Question

求11/2,21/4,31/8,41/16,⋯的前n项之和S_n

Answer 1

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

Sn=1+1/2+2+1/4+3+1/8+.+n+(1/2)^n;

=(1+2+3+.+n)+(1/2+1/4+1/8+.(1/2)^n);

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

明白,刚才复杂化了!