That is (1/an-1)1/a (n-1)-1=1/2.

So {1/an- 1} is a geometric series.

(2)1/an-1= (1/2) to the n power.

So 1/an=( 1/2) N+1 power.

So n/an = n +n power of n/2.

Let the original formula =Sn

Sn= 1/2+2/2？ ++n/2 to the power of n +(n+ 1)n/2 ①

Sn/2= 1/2？ +2/2? +...+(n-1)/2 to the n power +n/2 to the (n+ 1) power +(n+ 1)n/4 ②

(1)-(2) Get the n power of sn/2 =1/2+1-(1/2)/2-n/2+(n+ 1) n/4 (.

So the original formula =Sn=2-( 1/2) to the power of n -n/2 (n+2).