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Proof by induction 
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#1
May2109, 01:10 AM

P: 11

Use mathematical induction, to prove that [tex]\frac{n^{3}+5n}{3}[/tex]
is an even integer for each natural number n. I am fimilar with proof by induction but in most of the question that I have done have a LHS = RHS which seems to simplifiy things a little bit. Any help would be appreciated Cheers 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 


#2
May2109, 01:56 AM

HW Helper
P: 1,979

(n+1)^3 + 5(n+1) = n^3+3n^2+3n+1+5n+5 = (n^3+5n) + 3n(n+1) + 6. Now divide each term by 3 and see what kind of number you get. Since you are familiar with induction, this should be enough. 


#3
May2109, 02:30 AM

P: 11

Got it thanks mate



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