Consider the sequence,

a_n={1/2^n}

We need to show,

lim n--> oo a_n=0

By definition,

For all e>0 there is an N such that,

if n>N then, |a_n|=a_n<e

We note that,

0<=a_n<=1/n

And the limits of the sequenes,

lim n---> oo 0=0

lim n---> oo 1/n=0

Thus, by the Squeeze theorem for sequnces we have,

lim n---> oo a_n=0

Q.E.D.