Question 8 - A-Level Maths

Exam Board	OCR
Module	FP1 (Further Pure Mathematics 1)
Year	2013
Session	January
Topic	Partial Fractions
Type	Three linear factors in denominator

Show that \(\frac { 1 } { r } - \frac { 3 } { r + 1 } + \frac { 2 } { r + 2 } \equiv \frac { 2 - r } { r ( r + 1 ) ( r + 2 ) }\).
Hence show that \(\sum _ { r = 1 } ^ { n } \frac { 2 - r } { r ( r + 1 ) ( r + 2 ) } = \frac { n } { ( n + 1 ) ( n + 2 ) }\).
Find the value of \(\sum _ { r = 2 } ^ { \infty } \frac { 2 - r } { r ( r + 1 ) ( r + 2 ) }\).