1. Sigma Notation A compact way of defining a series A series is the sum of a sequence

2. Sigma - A Greek letter = ‘the sum of’ start term r=1 end term r=4 the sum of the first 4 terms Make r=1, r=2, r=3, and r=4 1 + 2 + 3 + 4= 10

3. = ‘the sum of’ start term r=1 end term r=6 the sum of the first 6 terms Make r=1, r=2, …, r=6 = 3 + 6 + 9 + 12 + 15 + 18 = 63

4. = ‘the sum of’ start term r=1 end term r=5 the sum of the first 5 terms Make r=1, r=2,...., r = 5 = 3 + 7 + 11 + 15 + 19 = 55

5. = ‘the sum of’ start term r=1 end term r=3 the sum of the first 3 terms Make r=1, r=2, r=3 = 7² + 9² + 11² = 49 + 81 + 121 = 251

6. Working in reverse - Write this series in sigma notation 1 + 4 + 9 + 16 + 25 = 1² + 2² + 3² + 4² + 5²

7. Working in reverse - Write this series in sigma notation 3 + 6 + 11 + 18 + 27 = (1² +2)+ (2²+2) + (3²+2) + (4²+2) + (5²+2) = (1+2) + (4+2) + (9+2) + (16+2) + (25+2)

8. Exercise 6B – Worked Solutions 1. Write down all the terms of the series (a) (b) (c) = 1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55 = (3×1-1)+(3×2-1) +(3×3-1) +(3×4-1) +(3×5-1) + (3×6-1) = 2 + 5 + 8 + 11 + 14 + 17 = 57 = (2×1²+3)+ (2×2²+3)+ (2×3²+3)+ (2×4²+3) = 5+ 11 + 21 + 35 = 72