OCR FP1 2005 June — Question 5

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2005
SessionJune
TopicSequences and series, recurrence and convergence
5
  1. Show that $$\frac { r + 1 } { r + 2 } - \frac { r } { r + 1 } = \frac { 1 } { ( r + 1 ) ( r + 2 ) }$$
  2. Hence find an expression, in terms of \(n\), for $$\frac { 1 } { 6 } + \frac { 1 } { 12 } + \frac { 1 } { 20 } + \ldots + \frac { 1 } { ( n + 1 ) ( n + 2 ) }$$
  3. Hence write down the value of \(\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( r + 1 ) ( r + 2 ) }\).
This paper (8 questions)
View full paper
Q1 Q2 Q3 Q4 Q5 Q6 Q8 Q9