A function f:R→Rf: \mathbb{R} \to \mathbb{R}f:R→R satisfies f(x)+f(y)=f(x+y)+xyf(x) + f(y) = f(x+y) + xyf(x)+f(y)=f(x+y)+xy and f(1)=2f(1) = 2f(1)=2. What is f(n)f(n)f(n) for n∈Z+n \in \mathbb{Z}^+n∈Z+?
f(n)=n2+3n2f(n) = \frac{n^2+3n}{2}f(n)=2n2+3n
f(n)=n2+1f(n) = n^2 + 1f(n)=n2+1
f(n)=n2+n2f(n) = \frac{n^2+n}{2}f(n)=2n2+n
f(n)=n2+nf(n) = n^2 + nf(n)=n2+n