It is proved that An+n=2A(n- 1)-2+2n is obtained by adding n to both sides at the same time.

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

Therefore, (an+n)/[a (n-1)+(n-1)] = 2.

So {An+n} is a geometric series with 2 as the first term and 2 as the common ratio.

(1) an+n = n power of 2

N -n power of An=2

(2)sn=2+2 twice +2 thrice +...+2 n times -( 1+2+3+4+)...+n)

= 2 (n times of 2-1)-1/2 n (1+n)