I've been given a homework question as follows:
Let $a$ be a positive real number, find a method to approximate $1/a$ without ever having to divide, with a sequence $x_k$ such that $x_k \to 1/a$. Explain why your solution works and and as much information as you can about the error. Hint. Think of a geometric series whose sum is $1/a$.
I've been going through all the series I can think of and my first question is, is there a way to create a geometric series whose sum is of your choice?
(I'm also finding it confusing how a sequence could converge to some number whilst the series also sums to that same number)