@acer Thanks a lot 

@Kitonum Thanks a lot 

@Carl Love  

what I meant here is that once i passes 0 and reashes to value 1 k gets added by 1 value as seen k+1. So when I insert a value in function sum2N(1) one value gets added from k and 1 from i after completing one cycle as seen (k+i)^2 which gives the value 4. The reason I did this kind of calculation becuase I was visualizing in my head that N^2 + (N+1)^2 and thought to make it (N+1)^2 as (k+i)^2 

@Carl Love