CSC_226_Midterm_3

CSC_226_Midterm_3 - = + + + + + + n4 2n3 n2 4n3 12n2 12n 44...

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6. P(n) : + + … + = [ + ] 13 23 n3 nn 12 2 Domain : {n| n ≥ 1} Basis: P(1) : = [ + ] = 13 11 12 2 1 (True) Proof: P(n + 1) : + + … + + + 13 23 n3 n 13 = [ + ] + ( + ) nn 12 2 n 1 3 (Inductive Hypothesis) = ( + ) + ( + ) n2 n 1 222 n 1 3 (Distribute Exponent) = + + + + + + n4 2n3 n24 n3 3n2 3n 1 (Distribute Exponent)
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Unformatted text preview: = + + + + + + n4 2n3 n2 4n3 12n2 12n 44 (LCD and Add) = + + + + n4 6n3 13n2 12n 44 (Add Like Terms) = ( + + ) n2 3n 2 222 (Factor Both Terms) = [ + + ] n2 3n 22 2 (Factor Out Exponent) = [ + ( + ) ] n 1 n 2 2 2 (Factor Numerator)...
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This note was uploaded on 04/28/2009 for the course CSC 226 taught by Professor Watkins during the Spring '08 term at N.C. State.

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