Analysis and Approaches for IBDP Maths Ebook 2 | Page 60

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 17
1. Prove by mathematical induction that
n
�
r�1
(2r
�1)
2
n n n
�
3
2
(4 �12 �11)
�
, n� .
[8]
�
2. Prove by mathematical induction that 1�1! � 2�2! � � n�n! � ( n �1)! � 1, n� .
[7]
3. Prove by mathematical induction that
�1� � 2 � � n� nn ( �1)
�
� � � � � � � � � � , n� .
�1� �1� �1�
2
[7]
4. Prove by mathematical induction that 1 3 � 2 3 � � n 3 � n
4 , n
�
� .
[7]
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