What’s on the Convergence Tests poster
A 7-row table: Test · Use when · Verdict.
Apply in order. Stop at the first that settles it.
- nth term — Always, first — aₙ not → 0 means diverges
- Geometric — Ratio r is constant — Converges iff |r| < 1
- p-series — Terms are 1/n^p — Converges iff p > 1
- Ratio — Factorials or powers — L < 1 converges, L > 1 not
- Comparison — Positive terms only — Bounded by a known series
- Alternating — Signs alternate — Needs decreasing and → 0
- Integral — f positive, decreasing — Series and integral agree
The ratio test is inconclusive at L = 1, which is exactly where the p-series live. Σ1/n diverges while Σ1/n² converges.
Questions about the Convergence Tests poster
- What’s on the Convergence Tests poster?
- A 7-row table: Test · Use when · Verdict. Apply in order. Stop at the first that settles it. nth term — Always, first — aₙ not → 0 means diverges; Geometric — Ratio r is constant — Converges iff |r| < 1; p-series — Terms are 1/n^p — Converges iff p > 1; Ratio — Factorials or powers — L < 1 converges, L > 1 not; Comparison — Positive terms only — Bounded by a known series; Alternating — Signs alternate — Needs decreasing and → 0; Integral — f positive, decreasing — Series and integral agree. The ratio test is inconclusive at L = 1, which is exactly where the p-series live. Σ1/n diverges while Σ1/n² converges.
- Who is the Convergence Tests poster for?
- Convergence Tests belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning calculus can pin it up — a beginner, a student mid-course, or someone revising years later.
- When should you use the Convergence Tests poster?
- Given an infinite series, work down this list and stop at the first test that decides. A wall chart earns its place by being glanceable from where the work is happening, so Convergence Tests belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Convergence Tests?
- The Chain Rule, Derivative Rules and Fundamental Theorem sit alongside Convergence Tests in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Chain RuleDerivative RulesFundamental Theorem
- Is the Convergence Tests poster free to download and print?
- Yes. Convergence Tests 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 Convergence Tests poster print at?
- Convergence Tests 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 Convergence Tests loses nothing.Printing guide
Related posters
Charts that sit alongside Convergence Tests on the same wall.
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