What’s on the Radius of Convergence poster?

5 numbered steps. For a series in powers of (x − a) with coefficients cₙ. Apply the ratio test — Take the limit L of |cₙ₊₁ / cₙ| as n grows, when that limit ex…; Invert to get R — R = 1/L. If L = 0 then R is infinite; if L is infinite then R = 0.; Write the open interval — The series converges absolutely whenever |x − a| < R.; Test both endpoints — At |x − a| = R the ratio test is silent. Substitute and test di…; State the full interval — The endpoints may be both included, both excluded, or one o…. Convergence is uniform on any closed interval strictly inside the radius, so term-by-term differentiation is valid there.

Who is the Radius of Convergence poster for?

Radius of Convergence 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 Radius of Convergence poster?

Every power series answer is incomplete until both endpoints are tested. A wall chart earns its place by being glanceable from where the work is happening, so Radius of Convergence belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.

What other posters go with Radius of Convergence?

Absolute vs Conditional, Bolzano-Weierstrass and Cauchy Sequences sit alongside Radius of Convergence in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.

Is the Radius of Convergence poster free to download and print?

Yes. Radius of Convergence 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.

What size does the Radius of Convergence poster print at?

Radius of Convergence 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 Radius of Convergence loses nothing.

Radius of Convergence — free printable poster

Radius of Convergence — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

Radius of Convergence, step by step

For a series in powers of (x − a) with coefficients cₙ.

Apply the ratio testTake the limit L of |cₙ₊₁ / cₙ| as n grows, when that limit exists.
Invert to get RR = 1/L. If L = 0 then R is infinite; if L is infinite then R = 0.
Write the open intervalThe series converges absolutely whenever |x − a| < R.
Test both endpointsAt |x − a| = R the ratio test is silent. Substitute and test directly.
State the full intervalThe endpoints may be both included, both excluded, or one of each.

Convergence is uniform on any closed interval strictly inside the radius, so term-by-term differentiation is valid there.

Questions about the Radius of Convergence poster

What’s on the Radius of Convergence poster?: 5 numbered steps. For a series in powers of (x − a) with coefficients cₙ. Apply the ratio test — Take the limit L of |cₙ₊₁ / cₙ| as n grows, when that limit ex…; Invert to get R — R = 1/L. If L = 0 then R is infinite; if L is infinite then R = 0.; Write the open interval — The series converges absolutely whenever |x − a| < R.; Test both endpoints — At |x − a| = R the ratio test is silent. Substitute and test di…; State the full interval — The endpoints may be both included, both excluded, or one o…. Convergence is uniform on any closed interval strictly inside the radius, so term-by-term differentiation is valid there.
Who is the Radius of Convergence poster for?: Radius of Convergence 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 Radius of Convergence poster?: Every power series answer is incomplete until both endpoints are tested. A wall chart earns its place by being glanceable from where the work is happening, so Radius of Convergence belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Radius of Convergence?: Absolute vs Conditional, Bolzano-Weierstrass and Cauchy Sequences sit alongside Radius of Convergence in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Absolute vs Conditional Bolzano-Weierstrass Cauchy Sequences
Is the Radius of Convergence poster free to download and print?: Yes. Radius of Convergence 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 Radius of Convergence poster print at?: Radius of Convergence 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 Radius of Convergence loses nothing.Printing guide

Radius of Convergence, step by step

Questions about the Radius of Convergence poster

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