Question 10 - A-Level Maths

Exam Board	OCR
Module	Further Pure Core 2 (Further Pure Core 2)
Year	2019
Session	June
Topic	Taylor series
Type	Maclaurin series for ln(trigonometric expressions)

Use differentiation to find the first two non-zero terms of the Maclaurin expansion of \(\ln \left( \frac { 1 } { 2 } + \cos x \right)\).
By considering the root of the equation \(\ln \left( \frac { 1 } { 2 } + \cos x \right) = 0\) deduce that \(\pi \approx 3 \sqrt { 3 \ln \left( \frac { 3 } { 2 } \right) }\). \section*{END OF QUESTION PAPER}