Analysis and Approaches for IBDP Maths Ebook 2 | Page 265

(e) (1) n�1� 1� � 1� An � � 4 d x (1) 4 n � � � � � � � � x� � n� �4 ln � n 1 4 1 � � � An � x � x � n � � � � n � 1 An � (4( n �1) � ln( n �1)) � (4n � ln n) � 4 � n 1 An � 4n � 4 � ln( n �1) � 4n � ln n � 4 � n 1 An � � ln n � ln( n � 1) n 1 n An � � ln n n�1 1 n �1 (2) An �1 � �ln n�1 n�2 1 n 1 n�1 (3) An � An� 1 � � ln � � ln n n �1 n �1 n � 2 n �1� n � n n �1� An � An� 1 � � ln � � � n( n �1) �n �1 n � 2 � 2n�1 n An � An� 1 � � ln n( n �1) n �2 (f) 13 13 e A � � ln 14 1 � 13 13 � ln � ln e � ln � � �1 14 1 1 � 13 13 � ln � ln e � ln � � �1 14 1 � 1 13 � ln � � ln � � �1 13 14 1 1 � � � 13 � � 13 20 www.seprodstore.com 255