Equation: X / 1 * 2 + X / 2 * 3 + X / 3 * 4 + '+ X / 19 * 20 is the solution of 19

Equation: X / 1 * 2 + X / 2 * 3 + X / 3 * 4 + '+ X / 19 * 20 is the solution of 19

Equation: X / 1 * 2 + X / 2 * 3 + X / 3 * 4 + '+ X / 19 * 20 is the solution of 19
x[1/1*2+1/2*3+.+1/19*20]=19
x[1-1/2+1/2-1/3+.+1/19-1/20]=19
x[1-1/20]=19
x*19/20=19
x=20