Subsequences of (a_n)=0?

Question

Give two distinct subsequences of the sequence (a_n), where for all n, a_n = 0.
This is from a past exam paper.

Answer 1

I am not sure quite what you mean what about
1. a(n) = sin(n*pi) which is zero when n belongs to the natural numbers.
2. a(n) = cos(n*(pi/2))

Answer 2

it incredibly is not authentic. evaluate the sequence 0, a million, 0, a million, 0, a million, ... each and every subsequence has a further subsequence 0, 0, 0, 0, ... which converges to 0, however the unique sequence does not converge.

Answer 3

1!-1!,2!-2!,3!-3!,...., 2007!-2007!,....

1-1,2-2,3-3,4-4,5-5,...,2007-2007,...