1. ## new convergence problem

let {a$\displaystyle _{n}$} and {b$\displaystyle _{n}$} be real sequences for every integer greater than or equal to 1. Suppose b$\displaystyle _{n}$ does not equal 0 for all integer n greater than or equal to 1. if {b$\displaystyle _{n}$} and {a$\displaystyle _{n}$/b$\displaystyle _{n}$} both converge, prove that {a$\displaystyle _{n}$} also converges.

So I am not sure what technique I am supposed to use in this problem. Can somebody help please? Thanks.

2. Originally Posted by janae77
let {a$\displaystyle _{n}$} and {b$\displaystyle _{n}$} be real sequences for every integer greater than or equal to 1. Suppose b$\displaystyle _{n}$ does not equal 0 for all integer n greater than or equal to 1. if {b$\displaystyle _{n}$} and {a$\displaystyle _{n}$/b$\displaystyle _{n}$} both converge, prove that {a$\displaystyle _{n}$} also converges.

So I am not sure what technique I am supposed to use in this problem. Can somebody help please? Thanks.
What are the properties of convergent sequences with relation to multiplication?

3. If {bn} and {an/bn} both converge, that implies that an = (an/bn) * bn converges, since it is a product of two convergent sequences.