- (a) Express \(\frac { 1 } { ( r + 3 ) ( r + 4 ) }\) in partial fractions.
(b) Hence, using the method of differences, show that
$$\sum _ { r = 1 } ^ { n } \frac { 1 } { ( r + 3 ) ( r + 4 ) } = \frac { n } { a ( n + a ) }$$
where \(a\) is a constant to be found.
(c) Find the exact value of \(\sum _ { r = 15 } ^ { 30 } \frac { 1 } { ( r + 3 ) ( r + 4 ) }\)
uestion 1 continued
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