Analysis and Approaches for IBDP Maths Ebook 2 | Page 275

Part IV – Sequence of the Quantity 2
(k) (1) Using the results of (g), find an inequality for
n
� Bk
.
k �1
n
e � 1
(2) Find lim
n 1 .
n��
e �
(3) Hence, show that
n
1 1
�lim� Bk
� .
2e
e
n��
k � 1
Consider the sequence B
1, B
3
, B
5
, …, B2n
� 1, ….
1 1 1 1 1 1
(l) (1) Find the exact value of � � � � � � .
2 3 4 5 6
e e e e e e
(2) Hence, show that 1 � B1 � B 1
3
� B5 � � B2 n �1
� �
2( e�1) e� 1
.
(m) (1) Express B
k
in terms of k .
(2) Hence, explain why B
k
is decreasing.
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