A-level Mathematics/OCR/FP1/Summation of Series

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Summation of a Series[edit]

In Core Two we learned about arithmetic and geometric progression, but if we need to sum an arithmetic progression over a large range it can become very time consuming. There are formulae that can allow us to calculate the sum. Note that these formulae only work if we start from 1; we will see how to calculate summations from other starting points in the example below. The formulae are:

We also need to know this general result about summation:

You can see why this is true by thinking of the expanded form:

Example[edit]

Find the sum of the series .

  1. First we need to break the summation into its three separate components.
  2. Next we need to make them start from one. We then need to subtract the sum of the numbers not included in the summation.
  3. Now we use the identities to calculate the individual sums. Remember to include the co-efficients.
  4. Now we need to perform a lot of arithmetic. This can be done by hand or utilizing a calculator.
  5. The sum of the series .


This is part of the FP1 (Further Pure Mathematics 1) module of the A-level Mathematics text.