Question

prove \(\lim\limits_{n\to\infty} a_n = m \implies \lim\limits_{n\to\infty}(c+a_n) = c+m \)

Answer 1

Need to show that for any \(\epsilon \gt 0\), there exists some \(N\) such that
\[n\gt N \implies |(c+a_n) - (c+m)| \lt \epsilon\]