Sequences and Series

Sigma notation

Sigma notation. Sigma notation is a method used to write out a long sum in a concise way. In this unit rules for using sigma notation are established.

Arithmetic and geometric progressions

Arithmetic and geometric progression. This unit introduces sequences and series, and gives some simple examples of each. It also explores particular types of sequence known as arithmetic progressions and geometric progressions, together with the corresponding series.

Limits of sequences

Limits of sequences. This unit introduces finite and infinite sequences, and explains what it means for two sequences to be the same and what is meant by the n-th term of a sequence. The divergence of an infinite sequence to plus or minus infinity, or its convergence to a real limit, is considered.

The sum of an infinite series

The sum of an infinite series. The partial sums of an infinite series form a new sequence. The limit of this new sequence (if it exists) defines the sum of the series. Two specific examples of infinite series that sum to e and pi respectively are described.

Limits of functions

Limits of functions. This unit explains what it means for a function to tend to infinity, to minus infinity, or to a real limit, as x tends to infinity or to minus infinity. A function which tends to a real limit as x tends to a given real number is also discussed.