A-level Mathematics/OCR/FP1/Summation of Series
Summation of a Series
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:
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 .