If f : R → R satisfies f ( x + y ) = f ( x ) + f ( y ) for all x , y ∈ R and f ( 1 ) = 7 , then ∑ r = 1 n f ( r ) is

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If $f : R \to R$ satisfies $f (x + y) = f (x) + f (y)$ for all $x, y \in R$ and $f (1) = 7$ , then $\sum_{r = 1}^{n} f (r)$ is

Answer:

Solution:

$f (1) = 7, f (2) = f (1 + 1) = f (1) + f (1) = 2 f (1), f (n) = n f (1)$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Functional Equation

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