Obtain the first four non-zero terms of the Taylor Series expansion of \cos x in ascending powers of (x - \frac{\pi}{4}).
The mark scheme is shown once you've answered.
Practise this question\{a_n\} is defined by a_1 = 1, a_{n+1} = 4 + 2\sqrt[3]{a_n}. Use mathematical induction to prove that 1 \le a_n \le 8 for all n in the…[6 marks]k > 0 and let f(k) = \frac{1}{k^2}. Show that f(k) - f(k+1) = \frac{2k+1}{k^2(k+1)^2}.[3 marks]\sum_{k=1}^n \left( \frac{1}{k^2} - \frac{1}{(k+1)^2} \right) = 1 - \frac{1}{(n+1)^2}.[5 marks]\sum_{k=1}^\infty \frac{2k+1}{k^2(k+1)^2} = 1.[3 marks]\cos(-\frac{\pi}{16}).[3 marks]More practice: the rest of this paper · more Series questions · all CAPE Pure Mathematics Unit 2 past papers