Question 13 - A-Level Maths

Exam Board	AQA
Module	Further Paper 2 (Further Paper 2)
Year	2024
Session	June
Marks	5
Topic	Sequences and series, recurrence and convergence

Use the method of differences to show that $$\sum _ { r = 2 } ^ { n } \frac { 1 } { ( r - 1 ) r ( r + 1 ) } = \frac { 1 } { 4 } - \frac { 1 } { 2 n } + \frac { 1 } { 2 ( n + 1 ) }$$ [5 marks]
13
Find the smallest integer $n$ such that $$\sum _ { r = 2 } ^ { n } \frac { 1 } { ( r - 1 ) r ( r + 1 ) } > 0.24999$$