Let f: R → R be a function which satisfies f(x + y) = f(x) + f(y) x, y R. If f(1) = 2 and g(n) = Σ k = 1 ^((n - 1)) f(k), n N then the value of n, for which g(n) = 20, is:

Sets, Relations and Functions: JEE Main 2020 Mathematics question

JEE Main 2020 · 2 Sep, Evening shift · Q3864

JEE Main 20202 Sep, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let f : R

\to

R be a function which satisfies f(x + y) = f(x) + f(y)

\forall

x, y

\in

R. If f(1) = 2 and g(n) =

\sum\limits_{k = 1}^{\left( {n - 1} \right)} {f\left( k \right)}

, n

\in

N then the value of n, for which g(n) = 20, is :