Analysis and Approaches for IBDP Maths Ebook 2 | Page 50

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Chapter
4
Binomial Theorem
SUMMARY POINTs
�
Properties of the combination coefficient
�n� 1. � � � 1
�0�
2.
3.
�n� � � � n
�1�
�n� n( n �1) ( n � r �1)
� ��
�r
� r!
for 2 �r�
n
�n�
� �:
�r
�
� Extended binomial theorem for x � 1:
n � n�
2 � n�
3
(1 � x) �1� nx � � � x � � � x �
� 2�
� 3�
n ( n)( n �1) 2 ( n)( n �1)( n � 2) 3
(1 � x) �1� nx � x � x �
(2)(1) (3)(2)(1)
Solutions of Chapter 4
40
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