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Let $f : \mathbb{R} \to \mathbb{R}$ be a function which satisfies $f(x+y) = f(x) + f(y)$, $\forall x, y \in \mathbb{R}$. If $f(1) = 2$ and $g(n) = \sum_{k=1}^{n-1} f(k)$, $n \in \mathbb{N}$, then the value of $n$, for which $g(n) = 20$, is:
(1) 5
(2) 20
(3) 4
(4) 9
Type: MCQ
$g(n) = n^2 - n = 20 \Rightarrow n = 5$
BETA
