2．（a）For the binomial expansion of \(\frac { 1 } { ( 1 - x ) ^ { 2 } } , | x | < 1\) ，in ascending powers of \(x\) ，
（i）find the first four terms，
（ii）write down the coefficient of \(x ^ { n }\) ．
（b）Hence，show that，for \(| x | < 1 , \sum _ { n = 1 } ^ { \infty } n x ^ { n } = \frac { x } { ( 1 - x ) ^ { 2 } }\) ．
（c）Prove that，for \(| x | < 1 , \sum _ { n = 1 } ^ { \infty } ( a n + 1 ) x ^ { n } = \frac { ( a + 1 ) x - x ^ { 2 } } { ( 1 - x ) ^ { 2 } }\) ，where \(a\) is a constant．
（d）Hence evaluate \(\sum _ { n = 1 } ^ { \infty } \frac { 5 n + 1 } { 2 ^ { 3 n } }\) ．