Show that, for all positive integers \(r\),
$$\frac { 1 } { ( r - 1 ) ! } - \frac { 1 } { r ! } = \frac { r - 1 } { r ! }$$
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Hence, using the method of differences, show that
$$\sum _ { r = 1 } ^ { n } \frac { r - 1 } { r ! } = a + \frac { b } { n ! }$$
where \(a\) and \(b\) are integers to be determined.