Chapter A.4, Problem 1E

To determine

To show: The sum of the functions $f_1\left(x\right),f_2\left(x\right),f_3\left(x\right)$ has the limit $L_1+L_2+L_3$, if the functions $f_1\left(x\right),f_2\left(x\right),f_3\left(x\right)$ have a limits $L_1,L_2,L_3$ respectively, as $x\to \infty$ and also to use mathematical induction to generalize the result to the sum of any finite number of functions.