Infinite Series and Convergence: Free Course

About this course

An infinite series is defined through the behavior of its partial sums. This course develops convergence tests, power series, Taylor approximations and error estimates. Study the complete public source playlist from Khan Academy in English, with all 70 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Distinguish sequences, series and partial sums.
• Choose and justify convergence tests.
• Find intervals of convergence for power series.
• Construct Taylor approximations and bound their errors.

Skills you’ll gain

• Convergence tests
• Power series
• Taylor polynomials
• Error bounds

Course Overview

Sequences and finite geometric sums supply the starting language, followed by infinite geometric series and counterexamples such as the harmonic series. Comparison, integral, ratio and alternating-series tests address different structures; the nth-term test provides a necessary condition without proving convergence by itself. Conditional and absolute convergence clarify what signs can change. Power-series lessons then examine intervals of convergence, differentiation and integration. Taylor and Maclaurin recordings connect function derivatives with polynomial approximations, while remainder bounds assess their accuracy. Proofs and worked examples remain together, including Euler's formula and identity. Selecting a test and checking its hypotheses matters as much as carrying out the algebra.

How to study the course

• Videos 1–17: this part of the source list includes “Proving a sequence converges using the formal definition” through “Worked example: finite geometric series (sigma notation)”. Identify the function, variable and conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 18–35: this part of the source list includes “Limit comparison test” through “Worked example: coefficient in Maclaurin polynomial”. Connect the method to the meaning of the problem. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 36–52: this part of the source list includes “Worked example: convergent geometric series” through “Convergent and divergent sequences”. Rework a demonstration with a changed parameter. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 53–70: this part of the source list includes “Series estimation with integrals” through “Power series of ln(1+x_)”. Check the result and explain its interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits learners with algebra and trigonometry preparation who want the specific calculus topic in the title. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort manipulating algebraic expressions and interpreting functions is important. Review the prerequisite calculus stated by a lesson before using an advanced technique.

Put the lessons into practice

Create a comparison table of several series and explain the test chosen for each. Include a case where the nth-term test is inconclusive. Build a polynomial approximation for a familiar function and state an error bound for a specific input. For a power series, check the interval endpoints separately instead of relying only on a radius calculation.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.