Analysis and Approaches for IBDP Maths Ebook 1 | Page 76

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Chapter
7
Binomial Theorem
� Properties of the n factorial n !:
�
1. n! � n�( n �1) �( n � 2) � �3�2�
1
2. 0! � 1
3. n! � n�( n � 1)!
Properties of the combination coefficient
1.
3.
SUMMARY POINTs
�n� n!
� � �
�r � r!( n � r)!
� n� � n �
� � �� � �n
�1� � n �1�
�n�
� �:
�r
�
� n�
� n�
2. � � �� � �1
� 0�
� n�
4.
� n n n( n 1) ( n r 1)
� � � �
� � � � �
� � �
� r � � n � r � r!
�
The binomial theorem:
�n� � n� � n� � n � � n�
( a � b)
� � �a b � � �a b � � �a b � � � �a b � � �a b
�0� �1� � 2� � n�1� � n�
�
n n 0 n�1 1 n�2 2 1 n�1 0 n
�n�
a
� �
n
n�r
r
� � � b , where the ( r �1)
r�0
r
�n�
-th term � � �a
�r
�
n�r
b
r
Solutions of Chapter 7
68
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