Thread: new convergence problem

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

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

Originally Posted by janae77

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

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