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Sigma notation
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The Greek letter Σ (sigma) is a short way to write a long sum.
Reading Σ
Σr=15 r2 means: put r = 1, 2, 3, 4, 5 into r2 and add.
= 1 + 4 + 9 + 16 + 25 = 55
The numbers at the bottom and top are the first and last values of r.
= 1 + 4 + 9 + 16 + 25 = 55
The numbers at the bottom and top are the first and last values of r.
Counting terms
Σr=520 has 20 − 5 + 1 = 16 terms. Always add 1.
Writing a sum with Σ
3 + 6 + 9 + ... + 60: each term is 3r, and 3r = 60 when r = 20.
So the sum is Σr=120 3r.
So the sum is Σr=120 3r.
Evaluate Σr=14 (2r + 1).
- r = 1, 2, 3, 4 give 3, 5, 7, 9
- 3 + 5 + 7 + 9
Answer: 24
Substitute each value of r from bottom to top and add. The number of terms is top − bottom + 1.
Check you have got it
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