Mathmatical Proof

Problem. Given a sequence {tn}, suppose

lim n→∞

tn = T, where T > 0.

Prove that

lim n→∞

1

tn =

1

T .

(Hint: You want to estimate ∣∣∣∣ 1tn − 1T ∣∣∣∣ .

You know ∣∣∣∣ 1tn − 1T ∣∣∣∣ = |tn −T||tn||T| ,

think about what to do next.)

1