Absolute vs ConditionalTwo kinds of convergent series, one of which survives rearrangement.MathematicsAbsolute convergenceΣ|aₙ| itself convergesIt implies Σaₙ convergesRearranging changes nothingProducts behave as you wouldhopeΣ(−1)ⁿ/n² is absolutelyconvergentConditional convergenceΣaₙ converges but Σ|aₙ| does notFragile: the order of termsmattersRearrangeable to any sum at allOnly the alternating test appliesΣ(−1)ⁿ/n is conditionallyconvergentTHE DIFFERENCE THAT MATTERSAbsolute convergence is a property of the terms; conditionalconvergence is a property of their order.Riemann's rearrangement theorem: a conditionally convergent seriescan be rearranged to reach any real number, or to diverge.Absolute vs Conditionallearnposters.com
Absolute vs Conditional — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Absolute vs Conditional poster

Absolute convergence against Conditional convergence, side by side.

Riemann's rearrangement theorem: a conditionally convergent series can be rearranged to reach any real number, or to diverge.

Questions about the Absolute vs Conditional poster

What’s on the Absolute vs Conditional poster?
Absolute convergence against Conditional convergence, side by side. Absolute convergence: Σ|aₙ| itself converges; Absolute convergence: It implies Σaₙ converges; Absolute convergence: Rearranging changes nothing; Absolute convergence: Products behave as you would hope; Absolute convergence: Σ(−1)ⁿ/n² is absolutely convergent; Conditional convergence: Σaₙ converges but Σ|aₙ| does not; Conditional convergence: Fragile: the order of terms matters; Conditional convergence: Rearrangeable to any sum at all; Conditional convergence: Only the alternating test applies; Conditional convergence: Σ(−1)ⁿ/n is conditionally convergent; Absolute convergence is a property of the terms; conditional convergence is a propert…. Riemann's rearrangement theorem: a conditionally convergent series can be rearranged to reach any real number, or to diverge.
Who is the Absolute vs Conditional poster for?
Absolute vs Conditional belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning analysis can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Absolute vs Conditional poster?
Before rearranging or multiplying series, or applying a term-by-term operation. A wall chart earns its place by being glanceable from where the work is happening, so Absolute vs Conditional belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Absolute vs Conditional?
Bolzano-Weierstrass, Cauchy Sequences and Compactness sit alongside Absolute vs Conditional in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Bolzano-WeierstrassCauchy SequencesCompactness
Is the Absolute vs Conditional poster free to download and print?
Yes. Absolute vs Conditional downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Absolute vs Conditional poster print at?
Absolute vs Conditional is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Absolute vs Conditional loses nothing.Printing guide

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