Prove that \[\lim_{x\to a}\,[f(x)+g(x)]=L+K.\]

Problem: 

Prove that
\[
\lim_{x\to a}\,[f(x)+g(x)]=L+K
\]
if
\[
\lim_{x\to a}\,f(x)=L
\]
and
\[
\lim_{x\to a}\,g(x)=K.
\]

Answer: 

It is true that \[\lim_{x\to a}\,[f(x)+g(x)]=L+K.\]