1.

Let xn= sin(n/6). Give the formula for a selection nk , such that the subsequence

(xnk)k is a constant sequence, with the constant, different to 0?

2.

Let xn be the sequence whose terms are, in order:

1,2,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,7,8,...

Determine whether each of the following is a subsequence of (xn).

1,2,3,4,5,6,...

1,2,2,3,3,3,4,4,4,4,...

1,2,2,3,3,4,4,5,5,6,6,...

1,3,2,4,3,5,4,6,5,7,...

1,3,5,2,4,6,3,5,7,4,6,8,...

1,5,4,8,7,11,10,14,...