5. Use the method of differences to prove that for \(n > 2\) $$\sum _ { r = 2 } ^ { n } \frac { 4 } { r ^ { 2 } - 1 } = \frac { ( p n + q ) ( n - 1 ) } { n ( n + 1 ) }$$ where \(p\) and \(q\) are constants to be determined.
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