Analysis and Approaches for IBDP Maths Ebook 2 | Page 270

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Part IV – Sequence of the Quantity 1
(l) (1) Using the results of (d), find an inequality for
n
� Ak
.
k �1
n
(2) Find lim
n�� 2 n � . 2
(3) Hence, show that
n
1
�lim� Ak
�1.
2
n��
k � 1
Consider the sequence A
2
, A
4
, A
6
, …,
A
2n
, ….
(m) (1) By considering the Maclaurin series of ln(1 � x)
, find the value of
1 1 1 1 1 1
� � � � � � , giving the answer in terms of ln 2 .
2 3 4 5 6 7
1
(2) Hence, show that (1 � ln 2) � A2 � A4 � A6 � � A2
n
� � 1 � ln 2 .
2
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