TOPIC 7: SEQUENCES & SERIES II (Σ Notation + MOD)

Question 1

Representation of a Series

Answer 1

n r=m Σ uᵣ

Question 2

5 Properties of the Σ Notation

Answer 2

1. Constant: (n-m+1) k
2. Constant * fn: Move constant to the front
3. Add/subtract: Can combine / separate
4. Change m to 1: n 1 MINUS m-1 1
5. uᵣ: r 1 MINUS r-1 1

Question 3

What’s the purpose of breaking down the Σ Notation using the properties?

Answer 3

To be able to find the summation through
1. AP
2. GP
3. Constant
4. Method of Differences

Question 4

What to show for using the method of differences?

Answer 4

1. Break down eqn to form X - Y
2. Show at least first 3 terms AND last 3 terms
3. Show cancellation

Question 5

When to use the method of differences?

Answer 5

1. Terms are out of AP/GP/constant e.g. log/ln
2. Fractions