mathematical proof

Question

Claim: If a(sub)n converges to A then (c+a(sub)n) converges to c+A

Answer 1

We can prove this using the rules of limits,

lim_n→∞ c = c if c is a constant

lim_n→∞ (c+a_n) = lim_n→∞ c + lim_n→∞ a_n = c+A