In mathematics a series is defined as the sum of a sequence of numbers. It can be express by using the notation ∑ a_n, where ∑ represents “sum” and “a_n” is the n-th term of the sum, which is a generalized way of expressing the terms of the sum.

∑ a_n= a_1+a_2+a_3+a_4+….+a_n

Since  ∑ a_n is a sum, we can group terms, change the order or the terms, without varying the result of ∑ a_n. (i.e.  ∑ a_n= a_4+a_3+(a_1+a_2)+….+a_n)

When writing ∑ a_n we also express the limits or the sum, in other words, we express when do we start adding (let’s say a_0)  and when do we finish (let’s say a_5). When we do this, ∑ a_n has an specific value. However, a sum can also have only one limit, this occurs when a sum starts a a point “n” but never ends. In this case, where the sum is infinite, two things can occur: The total sum will keep increasing to infinity (±∞)  and we say the series diverges, or the total sum can get close to a certain number k and we say the series converges to k.

The idea of a infinite series converging to a value k can be difficult to make sense, since it may seem that adding infinite terms would imply that the sum will always increase. This is true, however if the terms you add become smaller each time, then you don’t “progress” as much, in fact, let’s say you have 1 and you add +0.1+0.01+0.001+0.0001+…. then you never reach let’s say 2. You reach a number K (between 1 and 2).