Mathematical INductioN!!!! (1 Viewer)

[EvoRevolution]

(1) Use Mathematical induction to show that 5^(2n)-4^(2n)-3^(2n) is a multiple of 48 for all integers n>=1.


(2) Prove that n>=2 lines, no two of which are parallel and no three of which are concurrent have (n(n-1))/2 points of intersections.

 

[Drongoski]

 

[jet]

 

[Trebla]

(1) Use Mathematical induction to show that 5^(2n)-4^(2n)-3^(2n) is a multiple of 48 for all integers n>=1.


(2) Prove that n>=2 lines, no two of which are parallel and no three of which are concurrent have (n(n-1))/2 points of intersections.

It didn't specify to use induction in (2), so it would be valid to reason that since there are n lines, and two lines make up a point of intersection, then there are ⁿC₂ possibilities. Note that:
ⁿC₂ = n! / (n - 2)2!
= n(n - 1)(n - 2)! / 2 (n - 2)!
= n(n - 1) / 2

 

[jet]

I understand where youre coming from, and it is a good way of doing it, though I just thought that because the topic was mathematical induction thats what the OP wanted.