Mr. Integral

THE BIG IDEA

Sequences and Series

Can infinitely many contributions have a finite total?

A sequence tracks individual terms; a series tracks their running sums. Build that distinction first, then choose convergence tests from the terms’ structure and estimate the remainder when a test allows it.

Begin the first lesson →See the lesson route ↓

4 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Terms & partial sums
  2. bounding positive sums uses02Benchmarks
  3. factorials and powers suggest03Growth rates
  4. changing signs can provide04Alternating cancellation

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit4 lessons
  1. 01Sequences, Geometric and Telescoping SeriesDistinguish the limit of terms from the limit of their partial sums.
  2. 02Integral and Comparison TestsChoose a benchmark for a nonnegative series and use inequalities in the correct direction.
  3. 03Ratio and Root TestsUse exponential and factorial structure to test absolute convergence without overinterpreting the boundary case.
  4. 04Alternating Series and Error ControlDistinguish absolute from conditional convergence and bound a valid alternating remainder.