Analysis and Approaches for IBDP Maths Ebook 2 | Page 263

(b) (1) Find the area of the triangle CFG .
(2) Hence, show that 1 � A
1
2
� .
12 6
(c) Find an inequality for A
3
.
(d) Find an inequality for A
n
.
(e) (1) Express A
n
in terms of n .
(2) Write down the formula for An
� 1
.
2n�1
n
(3) Show that An
� An�
1
� � ln
n( n �1) n � 2
, n �
� .
(f)
Find � if
13 13 e
A �
� ln . 14
(g) Explain why A
k
is decreasing.
Part I Solution
(a) (1) The area of the rectangle ABCD
� (AD)(CD)
�� 1� � 1��
� (1) �� 4 � � � � 4 � ��
�� 2� � 1��
1
�
2
20
(2) The area of the triangle ACD
� 1 � 2 2
1
�
4
(3) 1 � A
1
1
�
4 2
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