Question 1 - A-Level Maths

Exam Board	CAIE
Module	Further Paper 1 (Further Paper 1)
Year	2021
Session	June
Topic	Sequences and series, recurrence and convergence

Show that $$\tan ( r + 1 ) - \tan r = \frac { \sin 1 } { \cos ( r + 1 ) \cos r }$$ Let $\mathrm { u } _ { \mathrm { r } } = \frac { 1 } { \cos ( \mathrm { r } + 1 ) \cos \mathrm { r } }$.
Use the method of differences to find $\sum _ { r = 1 } ^ { n } u _ { r }$.
Explain why the infinite series $u _ { 1 } + u _ { 2 } + u _ { 3 } + \ldots$ does not converge.