If \[f:R \to R\] satisfies \[f(x + y) = \[f(x) + \[f(y), for all x, y \[ \in \] R and \[f(1) = 7, then \[\sum\limits_{r = 1}^n {f\left( r \right)} \] is
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Official solution
\[f\left( {x + y} \right) = f\left( x \right) + f\left( y \right).\]
Function should be f(x)=mx
\[f\left( 1 \right) = 7;\]
\[\therefore\] m=7, \[f\left( x \right) = 7x\]
\[\sum\limits_{r = 1}^n {f\left( r \right)} = 7\sum\limits_1^n {r = {{7n\left( {n + 1} \right)} \over 2}} \]