# Proving null sequences

1. Apr 4, 2012

### rohan03

I know in general how to prove if sequence is null or not . But here is my confusion
- method in the text book I am reading - asks that to prove that any sequence is null we must show that for each ε>0, there is an integer N such that modulus of the given sequence is < ε, for all n>N

now I also understand this but my dilema is
taking modulu say for example given sequence is
{(1+(-1)^n)/(n+(-1)^n )}
taking modulus gives:
|(1+(-1)^n)/(n+(-1)^n )| is modulus 2/(n+1) ???

just not sure

2. Apr 4, 2012

### DonAntonio

$\left|\frac{1+(-1)^n}{n+(-1)^n}\right|=\left\{\begin{array}{cc}0\,&\,if\,\,n\,\,is\,\,odd\\\frac{2}{n+1}\,&\,if\,\,n\,\,is\,\,even\end{array}\right.$ , and of course the seq. begin with $n=2$.

DonAntonio

Ps. Of course, the absolute value has no relevance here...did you notice this?

3. Apr 4, 2012

### rohan03

Yes the question states n=2,3... So I am correct and must ignore negative values of n