X / 1 * 2 + X / 2 * 3 + X / 3 * 4 +... + X / 99 * 100 = 1 Is the final x = 100 / 99

X / 1 * 2 + X / 2 * 3 + X / 3 * 4 +... + X / 99 * 100 = 1 Is the final x = 100 / 99

x/1*2+x/2*3+x/3*4+...+x/99*100=1
x(1/1*2+1/2*3+1/3*4+...1/99*100)=1
x(1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100)=1
x(1-1/100)=1
x=100/99