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Unformatted text preview: last to next writing k k k k LHS = + + = + + + + = + + + + = + + + + + + = + + + + = + + + + ⋅ + + ⋅ + ⋅ = 2 1 ) 2 )( 1 ( ) 1 )( 1 ( ) 2 )( 1 ( 1 2 ) 2 )( 1 ( 1 ) 2 )( 1 ( ) 2 ( ) 2 )( 1 ( 1 1 ) 2 )( 1 ( 1 ) 1 ( 1 3 2 1 2 1 1 2 " Section 4.3 18. (6pts) Proof (by mathematical induction): Let the property P( n ) be “ n n 6 9 5 < + ” Base case: Prove P( n ) for n =2: LHS= 9 5 2 + and RHS= 2 6 . Thus 36 6 34 9 5 2 2 = < = + is true. Inductive hypothesis: For any integer 2 ≥ k assume P( k ) is true. That is, assume k k 6 9 5 < + Inductive step: Prove the property for 1 + = k n . That is we need to prove 1 1 6 9 5 + + < + k k . . RHS LHS k k k k k k = = ⋅ < ⋅ < + = + < + = + + + 1 1 1 6 6 6 6 5 ) 9 5 ( 5 45 5 9 5 (The first inequality is because 45 9 < and 2nd inequality is by inductive hypothesis. )...
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This note was uploaded on 04/29/2010 for the course MATH m325k taught by Professor Seckin during the Spring '10 term at University of TexasTyler.
 Spring '10
 seckin

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