Analysis and Approaches for IBDP Maths Ebook 1 | Page 86

Your Practice Set – Analysis and Approaches for IBDP Mathematics
2 2 4 3 2
(2n 1) (2n 3) 16n 64n 88n 48n
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3. (a) Show that � � � � � � � , where n� .
[3]
(b) Hence, or otherwise, prove that the product of the squares of any two consecutive
odd integers is odd.
[3]
2 2 2 2
n n n n n
4. (a) Show that � ( �1) � ( � 2) � 3( � 2 � 2) � 1, where n� .
[3]
(b) Hence, or otherwise, prove that the sum of the squares of any three consecutive
integers is smaller than a multiple of 3 by 1.
[3]
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