Series

"She cannot do Subtraction,” said the White Queen. “Can you do Division? Divide a loaf by a knife—what is the answer to that?” “I suppose—” Alice was beginning, but the Red Queen answered for her. “Bread-and-butter, of course."

Lewis Carroll

Sigma Notation

Prior Knowledge

Recognize all the basic functions
You must be able to manipulate algebraic expressions.
(If not, check this lesson)
You must be able to manipulate exponential expressions.
(If not, check this lesson)
You must be able to manipulate logarithmic expressions.
(If not, check this lesson)

Key Points

1. Watch the video:

2. Read this presentation
3. Watch this solved problem

Solved problem on Arithmetic Series

What you have to know:

How to find the nth term of an Arithmetic Sequence
(If not, check this lesson)

Key Points

1. Watch the video:

2. Read this presentation

Sum of infinite Geometric Series

Prior Knowledge

To be able to find terms and the sum of a geometric sequence.

Key Points

1. Watch the video:

2. Read this presentation

Financial applications of geometric sequences

What you have to know :

You must be calculate geometric series
(If not, check this lesson)
You must be able to Rearrange Formulae.
(If not, check this lesson)

Key Points

1. Watch the video:

Extra

Material and references:

Hodder Book SL(ISBN: 9781510462359) :
13A, 2B, 2C

Key Points

1. You should be able to work with arithmetic and geometric sequences given in sigma notation: \[ \sum_{r=1}^{n} u_r = u_1 + u_2 + u_3 + \cdots + u_n. \] The value of \( r \) at the bottom of the sigma (here \( r = 1 \)) shows where the counting starts, and the value of \( r \) at the top of the sigma (here \( r = n \)) shows where the counting stops.
2. You should be able to find the sum of infinite geometric sequences. For a geometric sequence with common ratio \( r \), \[ S_\infty = \frac{u_1}{1 - r}, \qquad |r| < 1. \]
3. You should be able to apply arithmetic and geometric sequences to real-world problems, often involving percentage change. A change of \( r\% \) is equivalent to multiplying by the factor \( 1 + \frac{r}{100} \). An annual inflation rate of \( i\% \) is equivalent to multiplying by \( \frac{1}{1 + \frac{i}{100}} \) each year to find the value in real terms.

IB Past Paper Problems

Select a topic and unit, then click the button below to get a new problem.

Choose a Topic: Choose a Unit:

Press the button to start!