Help Needed: Proving an Exercise Involving (1+sqrt(3))(2n+1)

[penguin007]

Hi everyone,

I'm studying an exercise and I got stuck. Indeed, I was asked to prove that:

E((1+sqrt(3))⁽²ⁿ⁺¹⁾)=(1+sqrt(3))⁽²ⁿ⁺¹⁾-(sqrt(3)-1)⁽²ⁿ⁺¹⁾

and I admit I haven't got a clue how to do it.

Any indication is welcome!

 

[statdad]

This is a probability question? What distribution is involved?

 

[penguin007]

No, it's not a probability question actually. E is the integer part of a number.