• Mathematics Extension 1
• Year 12

# Series and Applications, including Induction

approx. 13 hrs

7 topics

22 concepts

Enhance your proficiency with Series and Applications, including Induction, in preparation for your HSC examinations.

Available in
NSW

### Overview

This learning program covers the essential components of the Year 12 Advanced Series and Applications topic and Extension 1 Mathematical Induction topic as specified in the NSW Senior Mathematics Syllabus. Students who study Year 12 Series and Applications learn about Induction, apply appropriate techniques from the study of Series to solve problems and use inductive reasoning in the construction of mathematical proofs.

### Topics & Concepts We Cover

This learning program is made up of the following 7 topics, broken down into 22 concepts.

• #### General Series 1 concept

1. Derive a formula for the nth term of a series

• #### Sigma Notation 3 concepts

1. Use sigma notation to determine number of terms in a series

2. Convert from sigma notation to expanded form

3. Convert from expanded form to sigma notation

• #### Arithmetic Series 3 concepts

1. Sum of an arithmetic progression

2. Find the nth term of an arithmetic sequence

3. Identify that a sequence is an arithmetic sequence by finding a common difference

• #### Finite Geometric Series 3 concepts

1. Sum of a geometric series

2. Identify that a sequence is a geometric sequence by finding the common ratio

3. Find nth term of a geometric sequence

• #### Infinite Geometric Series 3 concepts

1. Finding the limiting sum of an infinite geometric series

2. Finding the rational form of a recurring decimal using infinite geometric series

3. Find the condition for an infinite geometric series to converge

• #### Application of Series 4 concepts

1. Miscellaneous application problems for arithmetic and geometric series

2. Annuities applications

3. Loan repayment applications

4. Compound interest applications

• #### Mathematical Induction 5 concepts

1. Proving the closed form of a series using induction

2. Proving divisibility using induction

3. Proving the closed form of first-order recurrence using induction

4. Principle of mathematical induction

5. Proving inequalities using induction

### What you'll get

Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Series and Applications, including Induction

Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime