Sequences and Series

Understanding Sequences and Series

• Comprehend the concept of sequences and their different types including arithmetic, geometric, and other special sequences.
• Understand the definition of a series, their types (for example, arithmetic series, geometric series), and their practical applications.
• Distinguish between finite and infinite sequences and series, recognising their key properties.

Sigma Notation

• Familiarise oneself with the sigma notation and the power it holds for succinctly indicating the sum of terms in a sequence or series.
• Acknowledge how to derive the formula for the sum of a finite arithmetic series using sigma notation.
• Utilise sigma notation in different contexts, including the calculation of the sum of a finite geometric series.

Limits of Sequence and Series

• Investigate the limit of a sequence and understand what it means for a sequence to converge to a limit.
• Explore the conditions under which a geometric series has a limit when the number of terms tends to infinity, and ascertain how to find this limit.
• Use appropriate tests to deduce whether a given series is convergent or divergent.

The Binomial Expansion in Relation to Sequence and Series

• Recognise the connection between the binomial expansion and sequences and series.
• Apply the binomial theorem to find a general term of a binomial expansion, even those involving fractional and negative indices.
• Apply the concepts of sequences and series to returns on investments, population growth and other real-world problems, using both simple and compound interest models.

Remember, it is important to understand the concepts and also practise problems from a wide range of resources for adequate revision. Don’t forget to solve past questions for a better understanding of the areas examiners often focus on.