10.3 Series
There is a great pizza place in my hometown that I used to visit quite a lot. There, each pizza is packed in a box that contains a pizza coupon. Ten pizza coupons can be exchanged for a free pizza. This begs the question: how much pizza do you get with a single purchase?
Immediately, you’ll receive a pizza. You’ll also get 1∕10-th of a pizza in the form of a coupon, making the “value” of the purchase at least 1 + 
pizzas.
However, upon exchanging ten coupons, you get another one. Thus, a coupon represents 
+ 
pizzas. Continuing with this logic, we’ll obtain that the true value of each purchase is
What is the value of this number? To find out, we’ll take a look at infinite series, a main pillar of mathematics. Infinite series (or series for short) are sums of the form
Adding infinitely many terms together might seem like a trivial matter, but I assure you, this is far from the truth. For instance, consider the sum
On...
