# new convergence problem

• Apr 23rd 2010, 07:19 PM
janae77
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.
• Apr 23rd 2010, 07:44 PM
Drexel28
Quote:

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?
• Apr 24th 2010, 07:44 AM
becko
If {bn} and {an/bn} both converge, that implies that an = (an/bn) * bn converges, since it is a product of two convergent sequences.