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

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< A-level Mathematics | OCR | FP1

## 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 .

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

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