Q13

In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$, the number of ways is $2$, i.e., $1+2, 2+1$. Give only the answer without any explanation.

In how many ways can a given positive integer $n \geq 3$ be expressed as the sum of $3$ positive integers (which are not necessarily distinct). For example, for $n=4$, the number of ways is $3$, i.e., $1+2+1, 2+1+1$ and $1+1+2$. Give only the answer without explanation.

In how many ways can a given positive integer $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.