7. (a) It is conjectured that $$\frac { 1 } { 2 ! } + \frac { 2 } { 3 ! } + \frac { 3 } { 4 ! } + \ldots + \frac { n - 1 } { n ! } = a - \frac { b } { n ! }$$ where \(a\) and \(b\) are constants, and \(n\) is an integer such that \(n \geq 2\). By considering particular cases, show that if the conjecture is correct then $$a = b = 1$$ (b) Use induction to prove that, for \(n \geq 2\), the following is true $$\frac { 1 } { 2 ! } + \frac { 2 } { 3 ! } + \frac { 3 } { 4 ! } + \ldots + \frac { n - 1 } { n ! } = 1 - \frac { 1 } { n ! }$$ [BLANK PAGE]