- (a) Express \(\frac { 3 } { ( 3 r - 1 ) ( 3 r + 2 ) }\) in partial fractions.
(b) Using your answer to part (a) and the method of differences, show that
$$\sum _ { r = 1 } ^ { n } \frac { 3 } { ( 3 r - 1 ) ( 3 r + 2 ) } = \frac { 3 n } { 2 ( 3 n + 2 ) }$$
(c) Evaluate \(\sum _ { r = 100 } ^ { 1000 } \frac { 3 } { ( 3 r - 1 ) ( 3 r + 2 ) }\), giving your answer to 3 significant figures.