An algebra problem by Mardokay Mosazghi

The sum of numbers between 1 and n is = (n(n+1))/2

1+2+3+.....+n=(n(n+1))/2 {formula}

we are looking for the sum of the even numbers between 1 and n so

2+4+6+.....+(n-1) n is ODD =1 2+2 2+2 3+......+2 ((n-1)/2) =2 (1+2+3+.....+ ((n-1)/2)) from the formula we obtain : =2 (((n-1)/2) ((n-1)/2+1))/2 =((n-1)/2) ((n+1)/2) =79 80 => (n-1) (n+1)=158 160 => n=159

If you divide each even number by 2 , then that would form a sequence as 1,2,3,.. to (n-1)/2. The sum of that progression would be (n-1)/2 (n+1)/2 which should be equal to 79 80. Only 159 satisfies the given equation.