Binomial Theorem

� Properties of the n factorial n !: 1 . n! � n�( n �1 ) �( n � 2 ) � �3�2�

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2 . 0 ! � 1 3 . n! � n�( n � 1 )!

� Properties of the combination coefficient

�n� n!

1 . � � _� �r � r!( n � r)!

�n� � �: �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

�n� -th term � _{� �a} �r

� n�r b r

Proofs and Identities

� Identity of x : The equivalence of two expressions for all values of x

� : Identity sign www . seprodstore . com

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