If f:R o 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 ight)} is

Question

If f:R 	o 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 ight)} is

Accepted Answer

Answer: A. {{7n\left( {n + 1} ight)} \over 2} f\left( {x + y} ight) = f\left( x ight) + f\left( y ight). Function should be f(x)=mx f\left( 1 ight) = 7; 	herefore m=7, f\left( x ight) = 7x \sum\limits_{r = 1}^n {f\left( r ight)} = 7\sum\limits_1^n {r = {{7n\left( {n + 1} ight)} \over 2}}

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

Answer

Explanation

More JEE Math questions