Specific examples do not prove the general case but one can use examples 
to gain insight that might lead to a proof of the general case.
To illustrate, Exercise 19 in Chapter 2 says to prove  
<i>(a<sup>-1</sup>ba)<sup>n</sup> = 
a<sup>-1</sup>b<sup>n</sup>a</i>.
When we write this out for the case that 
<i>n = 2</i> we see how the general case goes. In particular,
<i>(a<sup>-1</sup>ba)<sup>2</sup> =  
(a<sup>-1</sup>ba)(a<sup>-1</sup>ba)  
= (a<sup>-1</sup>bba)  
= (a<sup>-1</sup>b<sup>2</sup>a)</i>.
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Exercise 20 in Chapter 2 is another instance where doing the problem for 
the cases that <i>n = 2</i> and <i> n = 3</i> leads to a proof of the 
general case.