Edexcel F2 2016 June — Question 1

Exam BoardEdexcel
ModuleF2 (Further Pure Mathematics 2)
Year2016
SessionJune
TopicPartial Fractions
TypeQuadratic factor (difference of squares)
  1. (a) Express \(\frac { 1 } { 4 r ^ { 2 } - 1 }\) in partial fractions.
    (b) Hence prove that
$$\sum _ { r = 1 } ^ { n } \frac { 1 } { 4 r ^ { 2 } - 1 } = \frac { n } { 2 n + 1 }$$ (c) Find the exact value of $$\sum _ { r = 9 } ^ { 25 } \frac { 5 } { 4 r ^ { 2 } - 1 }$$
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