Question

Prove the following assertion:
For all natural numbers n≥1, the expression [(2^{n}+1)(2^{n}-1)/3(2^{n}+(-1)^{n})\] is a positive interger.

Answer 1

the question looks like this:
Prove the following assertion:\[(2^{n}+1)(2^{n}-1)/3(2^{n}+(-1)^{n})\]is a positive integer

Answer 2

(2^n +1)/3 , when n is odd which is positive for all valus of n..
again (2^n - 1)/3, when n is even , which is always positive if n>1.

Answer 3

thank you! Are there any particular steps to follow to make it a little clearer?

Answer 4

step 1. when n is odd..then (-1)^n=-1..
plug the value, u get (2^n +1)(2^n -1)/3(2^n -1) = (2^n +1)/3.
step 2, when n is even ...then (-1)^n= 1.
similarly plug this value...you will get (2^n -1)/3......
you got it???

Answer 5

I got it now, thanks :)