Question

If f : R→R satisfies f(x+y) = f(x) + f(y), for all x, y ∈ R, f(1) = 3/2 then ∑f(r) for (r = 1,n) 

is ...

(a) 3/2n(n + 1)

(b) 3(n + 1)/2

(c) 3n(n + 1)/4

(d) 3n/4

Answer 1

The correct option (c) 3n(n + 1)/4

Explanation:

= f(1) + (f(1) + f(1)) + (f(2) + f(1)) + (f(3) + f(1)) + ... + (f(n – 1) + f(1))