If f : ℝ → ℝ is such that f ( x + y ) = f ( x ) + f ( y ) for all x , y ∈ ℝ , f ( 1 ) = 7 and ∑ r = 1 n f ( r ) = 14112 , then

Step-by-step solution

We have f : ℝ → ℝ is such that f ( x + y ) = f ( x ) + f ( y ) for all x , y ∈ ℝ ,   f ( 1 ) = 7 . Now, f 2 = f 1 + 1 = f 1 + f 1 = 2 · 7 Similarly, f 3 = f 2 + 1 = f 2 + f 1 = 3 · 7 f 4 = f 3 + 1 = f 3 + f 1 = 4 · 7 ⋮       ⋮       ⋮ ⋮       ⋮       ⋮ ⋮       ⋮       ⋮ f n - 1 = 7 · n - 1 f n = n · 7 Therefore, &#