Have a quick question about taylor series. We covered taylor series somewhat in class, but there was a complete lack of explanation and our calculus book literally covers the topic in a single page. I understand the idea of a taylor series and how its related to a power series, but what I don't understand and neither does anyone else is why the k term in a taylor series is sometimes a k+1 etc as in why it changes. For example on some taylor series we will have (-1)^k but on others we will have (-1)^k+1 and for the factorial we will have k! or sometimes 2k! etc etc. Why does this happen? Just looking for someone to point me in the right direction or give an explanation. Also, are there any good summarized notes available online for the series tests, have a midterm in a few days and we have barely covered any of this stuff, so I'm kind of lost at this point.