- #1

- 11

- 0

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

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- #1

- 11

- 0

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

- #2

Homework Helper

- 1,981

- 4

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.

- #3

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- 0

Got it thanks mate

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