In my book it is talking about sequences and series and such. Finite and infinite and all that, and Im confused with what it says in the book. The book says, "If the terms of a finite sequence are added to obtain a finite sum, it is called a series. If a series is infinite, the sum up to any specified term is called a "partial sum". If the partial sums of any infinite series get closer and closer to a number k, so that by continuing the series you can make the sum as close to k as you please, then k is called the limit of the partial sums, or the limit of the infinite series. The terms are said to "converge" on k. If there is no convergence, the series is said to 'diverge'". The bolded part is the part I dont exactly follow. What I dont get is how it says the partial sums get closer to a number k? What does it mean there. I may just be thinking about it the wrong way.