Question

Prove If an and bn are convergent lim 1/bn = 1/ lim(bn)

Answer 1

To prove if two sequences are convergent, we can use the algebraic limit properties. Using these properties, we can show that if {an} and {bn} are convergent, then lim (1/bn) = 1/ (lim bn).

Step-by-step explanation:

To prove the statement, we can use the algebraic limit properties. Let's assume that {an} and {bn} are convergent sequences. We are given that lim (1/bn) = 1/ (lim bn). We need to prove this equality.

Using the algebraic limit properties, we have:

1. lim (1/bn) = 1 / (lim bn)
2. lim (1/bn) = lim (1 / bn)
3. lim (1/bn) = 1 / lim bn

Therefore, we have proved that if {an} and {bn} are convergent, then lim (1/bn) = 1/ (lim bn).