SELF DOUBT

Question

https://gateoverflow.in/510/gate1991-01-xv

 

IN THIS QUESTION I AM SOLVING LIKE THIS WE HAVE K COMPONENTS 1,2,3,.................K

EACH OF WHICH HAVE N₁,N₂,N₃,.................N_K VERTICES

SO TOTAL NUMBER OF EDGES ARE N₁(N₁-1)/2 +N₂(N₂-1)/2...................N_K(N_K-1)/2

SO AT SOMEWHERE IN STEPS I REACHED TO 1/2((-N)+N₁²+N₂².......N_K²))

NOT GETTING FURTHER FROM HERE ..................