​(r−1)<[r]≤r(2r−1)<[2r]≤2r(nr−1)<[nr]≤nr⇒(r−1)+(2r−1)+….+(nr−1)<[r]+[2r]+…+[nr]≤r+2r+……+nr⇒r(2n(n+1)​)−n<[r]+[2r]+…+[nr]≤r(2n(n+1)​)⇒n→∞lim​r2(n(n+1))​−nn2⇒2r​