3．A sequence \(\left\{ u _ { n } \right\}\) is given by $$\begin{aligned} u _ { 1 } & = k & &
u _ { 2 n } & = u _ { 2 n - 1 } \times p & & n \geqslant 1
u _ { 2 n + 1 } & = u _ { 2 n } \times q & & n \geqslant 1 \end{aligned}$$ where \(k , p\) and \(q\) are positive constants with \(p q \neq 1\)
（a）Write down the first 6 terms of this sequence．
（b）Show that \(\sum _ { r = 1 } ^ { 2 n } u _ { r } = \frac { k ( 1 + p ) \left( 1 - ( p q ) ^ { n } \right) } { 1 - p q }\) In part（c） \([ x ]\) means the integer part of \(x\) ，so for example \([ 2.73 ] = 2 , [ 4 ] = 4\) and \([ 0 ] = 0\)
（c）Find \(\sum _ { r = 1 } ^ { \infty } 6 \times \left( \frac { 4 } { 3 } \right) ^ { \left[ \frac { r } { 2 } \right] } \times \left( \frac { 3 } { 5 } \right) ^ { \left[ \frac { r - 1 } { 2 } \right] }\)