Sets, Relations & Functions · Functional equations

Let for some

\alpha \in \mathbb{R}

f : \mathbb{R} \to \mathbb{R}

be a function satisfying

f(x + y) = f(x) + 2y^2 + y + \alpha xy

for all

x, y \in \mathbb{R}

. If

f(0) = -1

and

f(1) = 2

, then the value of

\displaystyle\sum_{n=1}^{5}\left(\alpha + f(n)\right)

is:

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