Analysis and Approaches for IBDP Maths Ebook 2 | Page 272

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(3)
(m) (1)
n
n
n
lim �lim�
A �lim
2( 1) n�1
k
n�� n�
n�� n��
k�1
n
n
n
lim �lim�
A �2lim
2 2 2n�2
k
n�� n�
n�� n��
k�1
n
1 �1�
�lim�
Ak
�2
2 n�� � �
k � 1 �2�
n
1
�lim�
Ak
�1
2
n��
k � 1
2 3
x x
ln(1 � x)
� x� � �
2 3
1 1 1 1 1 1
ln(1 �1) �1� � � � � � �
2 3 4 5 6 7
1 1 1 1 1 1
�ln 2 � �1� � � � � � �
2 3 4 5 6 7
1 1 1 1 1 1
� � � � � � �1�
ln 2
2 3 4 5 6 7
(2) 1 � A
1
2
�
12 6
1 � A
1
4
�
40 20
1 � A
1
6
�
84 42
…
1 1
� A2
n
�
2(2 n)(2n �1) 2 n(2n
�1)
…
1 1 1 1
� � � � � �
12 40 84 2(2 n)(2n�1)
1 1 1 1
� A2 � A4 � A6 � � A2
n
� � � � � � �
6 20 42 2 n(2n�1)
1 �1 1 1 1 �
� � � � � � �
2 �6 20 42 2 n(2n�1)
�
1 1 1 1
� A2 � A4 � A6 � � A2
n
� � � � � � �
6 20 42 2 n(2n�1)
1 �1 1 1 1 1 1 1 1 �
� � � � � � � � � � �
2 �2 3 4 5 6 7 2n
2n�1
�
1 1 1 1 1 1 1 1
� A2 � A4 � A6 � � A2
n
� � � � � � � � � � �
2 3 4 5 6 7 2n
2n�1
1 (1 � ln 2) � A 1 ln 2
2
� A4 � A6 � � A2
n
� � �
2
262
SE Production Limited