If 1 1 + 2 + 1 2 + 3 + + 1 99 + 100 =m and 1 1 2 + 1 2 3 + + 1 99 100 =n , then the point ( m , n ) lies on the line

Step-by-step solution

aligned & 1 1 + 2 + 1 2 + 3 + + 1 99 + 100 = m & 1 - 2 -1 + 2 - 3 -1 99 - 100 -1 = m aligned aligned & 100 -1= m m =9 & 1 1 2 + 1 2 3 + 1 99 100 = n & 1 1 - 1 2 + 1 2 - 1 3 1 99 - 1 100 = n & 1- 1 100 = n & 99 100 = n & ( m , n )= (9, 99 100 ) & 11(9)-100 ( 99 100 ) & =99-99=0 aligned Ans. 11 x-100 y=0