Analysis and Approaches for IBDP Maths Ebook 2 | Page 271

Part IV Solution
(l) (1) 1 � A
1
1
�
4 2
� A
1
2
�
12 6
� A
1
3
�
24 12
…
1 1
� A n
�
2 n( n �1) n( n �1)
1 1 1 1
� � � � �
4 12 24 2 nn ( �1)
1 1 1 1
� A1 � A2 � A3
� � An
� � � � �
2 6 12 nn ( �1)
n
1 �1 1 1 1 � 1 1 1 1
� � � � � �� � Ak
� � � � �
2 �2 6 12 n( n �1) � k�1
2 6 12 n( n �1)
1 �1 1 1 1 1 1 1 1 �
� � � � � � � � � �
2 �1 2 2 3 3 4 n n�1�
n
1 1 1 1 1 1 1 1
� � Ak
� � � � � � � � �
1 2 2 3 3 4 n n � 1
k �1
n
1 �1 1 � 1 1
� � �� � Ak
� �
2 �1 n�1�
k�1
1 n�1
n
1 �n�1 1 � n�1 1
� � �� � Ak
� �
2 �n �1 n �1�
k�1
n �1 n �1
n
n
n
��
Ak
�
2( n�1) n�1
k�1
20
(2)
n 1
lim � lim
n��
2n
� 2 n��
2
2 �
n
n 1
lim �
n��
2 n � 2 2 � 0
n 1
lim �
n��
2 n � 2 2
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