Calculate in C programming language the recursive sum of S=1/2+2/1+2/3+3/2+...+n/(n+1)+(n+1) /n

1. define independent-set as the problem that takes a graph g and an integer k and asks whether g contains an independent set of vertices of size k. that is, g contains a set i of vertices of size k such that, for any v and w in i, there is no edge (v,w) in g. show that independent-set is np-complete.