Sequences (Calculus 3)

Question

State whether the following statement is True or False. If True, state a relevant theorem from where it follows. if False, give a counter-example.

If a_n and b_n are any two sequences such that a_n + b_n is bounded, then both a_n and b_n must be bounded.

Answer 1

This is false.

The counter-example: a_n =n, b_n = 1 - n