P( ): . + , which is true. Thus, P( n ) is true for n = . Assume that P( k ) is true for some natural number k , i.e., ...
( ) We need to prove that P( k + ) is true whenever P( k ) is true. We have ... . .
. ) )( ) k k k k )( ) k k k k [Using ( )] PRINCIPLE OF MATHEMATICAL INDUCTION ) )( ) k k k k ) )( ) k k k k