Question 6 - A-Level Maths

Exam Board	OCR
Module	Further Pure Core 1 (Further Pure Core 1)
Year	2018
Session	September
Topic	Sequences and series, recurrence and convergence

Find as a single algebraic fraction an expression for \(\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 2 r - 1 ) ( 2 r + 1 ) }\).
Determine the value of \(\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( 2 r - 1 ) ( 2 r + 1 ) }\).