- (a) Use the method of differences to prove that for \(n > 2\)
$$\sum _ { r = 2 } ^ { n } \ln \left( \frac { r + 1 } { r - 1 } \right) \equiv \ln \left( \frac { n ( n + 1 ) } { 2 } \right)$$
(4)
(b) Hence find the exact value of
$$\sum _ { r = 51 } ^ { 100 } \ln \left( \frac { r + 1 } { r - 1 } \right) ^ { 35 }$$
Give your answer in the form \(a \ln \left( \frac { b } { c } \right)\) where \(a , b\) and \(c\) are integers to
be determined.