*Warning*-This is not a formal proof but it captures the idea.Originally Posted by nertil1
Let,
Thus,
Let,
Thus,
Thus,
Thus,
But,
because it is an infinite geometric series,
Thus,
I am having difficulty solving this math problem:
Suppose it is known that |x| < 1. What then is the sum from n=1 to n=infinity of nx^n?
I know how to do it if there is a constant in front of the x, but I don't know what to do since there's a variable in front of it.
Anybody have any ideas, it's really starting to annoy me?
Thanks a Lot
-Nertil
I was thinking about another way of doing this problem.
Notice the partial sums,
=
In general,
All of this is a manipulation of the geometric series,
As you take the limit the exponents die,
Thus,
But that is the geometric series thus,
This proof is more formal.