• Support PF! Buy your school textbooks, materials and every day products Here!

Proof by induction

  • Thread starter asset101
  • Start date
  • #1
11
0
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

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Shooting Star
Homework Helper
1,977
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
11
0
Got it thanks mate
 

Related Threads for: Proof by induction

  • Last Post
Replies
6
Views
723
  • Last Post
Replies
2
Views
881
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
591
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
4
Views
3K
Top