1. Basic Sigma Notation and RulesSo
So r starts at 1 and increases up to a finishing value of n
Addition rule:
where vr denotes rth term of sequence
Constant Multiple rule:

2. Using the addition and multiplication rules

3. Changing the signs in a series
The term (-1)r means that all the odd terms in the series are –ve
The term (-1)r+1 means that all the odd terms in the series are +ve

4. i.e = 15
i.e = 6
i.e = 14
i.e = 36

5. Difference Method
1) Express the expression g(r) you are trying to sum as
g(r) = f(r+1) – f(r) or f(r) – f(r+1)
2) Substitute values from 1 to n into this expression and
determine the sum after cancelling the relevant terms.
This is in the form g(r) = f(r) - f(r+1)
f(r) =
f(r+1) =

6. So g(r) = f(r) – f(r+1)
with g(r) = , f(r) = and f(r + 1) =

7. The terms which remain are 1 - which simplifies to

8. Questions involving Factorials
Exam qu.
Show that (r + 2)! – (r + 1)! = (r + 1)2  r!
Hence find 221! + 32  2! + 42  3! …………(n + 1)2  n!
(r + 2)! = (r + 2)(r + 1)(r )(r – 1)…….. = (r + 2)(r + 1)r!
(r + 1)! = (r + 1) (r )(r – 1)…….. = (r + 1)r!
So (r + 2)! – (r + 1)! = (r + 2)(r + 1)r! – (r + 1)r!
= (r)!(r+1)((r + 2) –1)
= r!(r+1)2

9. = (n + 2)! – 2!