question_answer

If \[f:R\to R\] satisfies \[f\left( x\text{+}y \right)=f\left( x \right)+f\left( y \right),\] \[\forall x,\] \[y\in R\] and f(1)= 11, then \[\sum\limits_{r=1}^{n}{f(r)}\] is _______.

A)  \[\frac{11\,n\,(n+1)}{2}\]          

B)  \[\frac{11\,n}{2}\]

C)  \[11{{n}^{2}}\]                                 

D)  \[\frac{11\,{{n}^{2}}}{2}\]

E)  None of these