Please help me solve these two problems. To be honest, I would really appreciate something more than just a small hint, because I have really no idea how to go about solving it ;(

1. Consider all possible sequences of natural numbers whose sum is $\displaystyle n$ . Each sequence has a certain number of terms. How many terms appear in all those sequences.?

2. Consider all possible sequences of natural numbers whose sum is $\displaystyle n$ . Find the number $\displaystyle t(n,k)$ , which represents the number of times a certain natural number $\displaystyle k$ appears in such sequences.