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Proof by induction

by asset101
Tags: induction, proof
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asset101
#1
May21-09, 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
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Shooting Star
#2
May21-09, 01:56 AM
HW Helper
P: 1,979
Quote Quote by asset101 View Post
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...
Put n+1 in place of n.

(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.
asset101
#3
May21-09, 02:30 AM
P: 11
Got it thanks mate


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