Question

Is this a valid math formula:

Answer 1

\[\frac{1}{a*b} = \frac{1}{a}-\frac{1}{b}\]

Answer 2

I ask because my textbook has this step in its proof:
\[1 + \frac{1}{2*1} + \frac{1}{3*2} + \frac{1}{4*3} +... + \frac{1}{(m-1)m}\]
is equivalent to
\[1 + (1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3}-\frac{1}{4}) +...+(\frac{1}{m-1}-\frac{1}{m})\]