Question 3
Let $f(n)$ be the sum of the first $n$ terms of the sequence
$$
0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, \ldots
$$
a) Give a formula for $f(n)$.
b) Prove that $f(s+t)-f(s-t)=s t$ where $s$ and $t$ are positive integers and $s\gt t$.
$$
0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, \ldots
$$
a) Give a formula for $f(n)$.
b) Prove that $f(s+t)-f(s-t)=s t$ where $s$ and $t$ are positive integers and $s\gt t$.