Breaking fractions

Algebra Level 2

The following two equations are true: \[ \begin{array} { r c l } \dfrac 11 - \dfrac12& =& \dfrac1{1\times2} \\ \dfrac 11 - \dfrac12 -\dfrac13 &=& \dfrac1{1\times2\times 3}. \end{array} \] Is it also true that \[ \dfrac 11 - \dfrac12 -\dfrac13 - \dfrac14 = \dfrac1{1\times2\times 3\times4} ? \]