TITLE: Sum of rational numbers
QUESTION [6 upvotes]: The sum of a finite number of rational numbers is of course a rational number, but the sum of an infinite number of rational numbers might be an irrational number.  Can someone give me some intuition why this sum might be irrational?  I just "don't feel it."

REPLY [5 votes]: Dear I am thinking about it because I am also a student of Mathematics.
We know that $e$ is an irrational number.
The value of $e$ is
$$= 1 + \frac{1}{1} + \frac{1}{2!} + \frac{1}{3!} + \ldots$$
$$= 1 + \frac{1}{1} + \frac{1}{2} + \frac{1}{6} + \frac{1}{24} + \ldots$$
$$= 2.7182 \ldots$$ (Irrational Number)
So sum of infinite rational numbers may be irrational.