• 322 Basic null sequences
ᐥThe following are null sequences. ❶ ｢1/n˄p｣ for p>0 ❷ ｢c˄n｣ for |c|<1 ❸ ｢n˄p·c˄n｣ for p>0 and |c|<1 ❹ ｢c˄n/n!｣ for c∈ℝ ❺ ｢n˄p/n!｣ for p>0ᐥ Proof of ❶ ∀ε>0 ∃N∈ℕ such that N > 1/ε. n > N ⇒ n > 1/ε ⇒ 1/n < ε ⇒ |1/n−0| < ε ｢1/n｣ is a null sequence. By the p ...
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