### Archive

Archive for November, 2016

## On Convergent Sequences

So here's a question that I've been preoccupied with in the last couple of days.  Suppose I have a convergent (at the sum) sequence, if you like a geometric sequence, say $1/2, 1/4, 1/8, ... = 1$.  If one were to multiply the elements of the sequence by its corresponding index, would this still be a convergent sequence? In this case, I'm concerned with $1/2 * 1, 1/4 * 2, 1/8 * 3, ...$ and its convergence (at the sum).  I wish to explore whether there are particular circumstances in which this is indeed the case.