Telescoping series

A telescoping series is like doing a hundred-piece multiplication problem one piece at a time. Instead of having to do all one hundred pieces in one big calculation, you can do it in sections, adding a little bit with each step and eventually getting the end result. For example, if you needed to find the sum of all the numbers from 1 to 100, instead of adding all 100 together, you could start with 1 + 2 = 3, then 3 + 3 = 6, then 6 + 4 = 10 and so on, until you got to 100. This is a telescoping series.