Math Is Fun Forum

Hey guys, I am learning about trees and one of the questions from my book what to prove that all trees are bipartite (so they are 2-colorable). I did this fine by induction but the next question says:

"Are all trees therefore planar?" Explain your answer.

I am not sure how to go about this. Any help would be awesome, thanks.

Hi everyone, I need some help on some sequences questions. I tried them, but failed bad.

1. Prove that the function:

converges whenever the following holds: 

2.

If

for all

and

, then what are the

?

Any help on either of these question would be greatly appreciated. I tried 1, but I could not get the limit to evaluate to a finite number, I must be doing it wrong.

Hey everyone, I am finding induction a bit hard so if anyone could help me with these 2 questions it would be much appreciated.

Use strong mathematical induction to prove that there exists positive integers a, b, c satisfying

for

.

Using mathematical induction, prove that any positive integer a may be expressed as a sum of Fibonacci numbers

where none of the

's are repeated in the sum.

If you could show me what to do that would be great.
Thanks

Hey everyone, can anybody help me out here, I don't know what the dual of a regular 27-gon is.

Thanks

Hi, I need help on a problem from my discrete math textbook.

If

is a polynomial with integer coefficients, and that this polynomial takes the value zero at four distinct integer values a, b, c and d.

Show that there exists no integer value n for which

.

I don't know how to do it and my book doesn't go through it well enough. Can anyone help me?

Thanks