1
Q
Series
A
A sum of terms
2
Q
How is a series written
A
upper bound
Σ expression
variable = lower bound
3
Q
n
Σ 1
r = 1
A
n
4
Q
n
Σ r
r = 1
A
1/2 n(n+1)
5
Q
n
Σ r^2
r = 1
A
1/6 n(n+1)(2n+1)
6
Q
n
Σ r^3
r = 1
A
1/4 n^2 (n+1)^2
7
Q
How to carry out a series if the lower bound isn’t 1
A
Carry out from 1 to the upper bound
Carry it out from 1 to ONE LESS than the lower bound
Subtract the second from the first
Write out the functions as you may be able to take out a factor
8
Q
n
Σ kr
r = 1
A
n
k Σ r
r = 1
9
Q
What to do if your expression has more than one part
A
Separate them by powers of r and treat as separate series
10
Q
What do you do when manipulating?
A
Always look to factorise where possible
