find the sum of r from 0 to n of : 1/((r+1)(r+2)(r+3))

The solution like almost every Methods of Differences questions first involves putting the fraction into partial sums.At this point you would get 3 fractions which can be tricky to deal with. Following what my teachers taught me you can then list out the terms starting from 0 and try to find a pattern and then try to cancel terms. From my class' experience in a mock test with this type of question, doing this method usually ends in confusion and a lot of time wasted.My solution which involves splitting the second term into 2 and then treating the problem as 2 separate Methods of Differences questions and then adding them up later. It's not the most complex problem you can find but I wanted to show that often times in A level Mathematics a seemingly difficult problem can be made easy if you find a way to break it down into questions you are comfortable in solving.