If , with , , and , find _ n _ r=1 ^ n (4r)f(3r) n^3…

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

f(x+y+z)=f(x)+f(y)+f(z)

, with

f(1)=1

f(2)=2

, and

x,y,z\in\mathbb{R}

, find

\lim_{n\to\infty}\sum_{r=1}^{n}\frac{(4r)f(3r)}{n^3}.