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

Question

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

TestHub · Accepted Answer

f ( x + y ) = f ( x ) + f ( y ) . Let f ( α ) = m α f ( 1 ) = 7 ; ∴ m = 7 , f ( x ) = 7 x ∑ r = 1 n ​ f ( r ) = 7 ∑ 1 n ​ r = 2 7 n ( n + 1 ) ​

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