Master AP Calculus BC Series with SERIES Pro for TI-84 Plus CE

📌 Prefer the full bundle? Get the AP Calculus BC Bundle.

🧮 What Is SERIES Pro?

SERIES Pro is your all-in-one AP Calculus BC series reference program for the TI-84 Plus CE and TI-84 Plus CE Python.
It walks you through everything you need for the Series unit — from identifying convergence tests to building Taylor and Maclaurin series approximations.

Unlike most calculator programs, SERIES Pro doesn’t simply display formulas — it guides you step by step with on-screen explanations, decision trees, and examples.

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⚙️ What It Covers

SERIES Pro is organized by concept, so you can instantly find what you need:

Convergence Tests

• GPART method → Geometric, p-Series, Alternating, Ratio, Root/Comparison/Integral.

• Walk-through of when and why to use each.

• Visual error-bound examples.

Common Series

• Geometric, p-Series, Harmonic, Exponential, Logarithmic, and Factorial series.

• Includes convergence criteria and sample sums (π²/6, ln 2, etc.).

Taylor & Maclaurin Series

• Built-in expansions for eˣ, sin x, cos x, ln(1 + x), 1/(1 – x), arctan x.

• Error bounds and radius/interval of convergence guides.

Calculators & Practice Tools

• Partial-sum calculator.

• Error-bound and approximation tools.

• Quick sequence term finder (arithmetic, geometric, factorial, power).

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🧠 Why Students Love It

• Saves time deciding which test to use.

• Reduces errors with clear criteria and reminders.

• Perfect for study and practice, even if your teacher allows reference programs on tests.

• Pairs beautifully with the upcoming AP Calculus BC Bundle, which will include Derivatives, Integrals, and Polar/Parametric modules.

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🧩 What’s Coming Next

SERIES Pro is the first module in the AP Calculus BC Bundle, which will include:

• Calculus Formula Guide (basic derivatives + integrals)

• Series Pro (this program)

• Derivatives Library with step-by-step examples

• Integrals Library with worked patterns

• Polar & Parametric Program for BC-specific topics

Buy SERIES Pro today and you’ll automatically receive a free upgrade to the AP Calculus BC Bundle when it launches.

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🖥️ How to Install

1. Download the .8xp file from mcstutoring.com/products/series-pro.

2. Connect your TI-84 Plus CE with TI Connect™ CE software.

3. Drag and drop the file onto your calculator.

4. Run SERIESPRO from the PRGM menu.

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🎓 Perfect for Students Who…

• Are currently taking AP Calculus BC or Calculus II.

• Want a refresher on series tests and Taylor/Maclaurin expansions.

• Prefer clear on-screen guidance over memorizing dozens of tests.

• Use their TI-84 Plus CE daily for homework or exam prep.

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📦 What’s Included

• SERIESPRO.8xp program file.

• Quick-start instructions.

• Free lifetime updates (you’ll get the BC bundle additions automatically).

Why Students Struggle with Series

Most BC students approach series problems with trial and error:

• "Maybe I'll try the ratio test first?"
• "Does this look like a p-series?"
• "I think this alternates... or does it?"

This random approach wastes precious exam time and leads to frustration. There's a better way.

Introducing the GPART Method™

After 25+ years of teaching AP Calculus BC, I've developed a strategic approach that gives students a clear roadmap for every series problem. The GPART Method tells you exactly which test to try first, saving time and boosting confidence.

G - Geometric Series (Try This First)

Look for: Constant ratio between consecutive terms

Form: ∑ ar^n or ∑ a·r^(n-1)

Decision: |r| < 1 → Converges with sum = a/(1-r)

Example: ∑(3/4)^n from n=0 to ∞

• Ratio r = 3/4, |r| = 3/4 < 1 ✓
• Converges with sum = 1/(1-3/4) = 4

P - p-Series (Check for 1/n^p Pattern)

Look for: Terms in the form 1/n^p

Decision: p > 1 → Converges, p ≤ 1 → Diverges

Example: ∑(1/n^1.5) from n=1 to ∞

• p = 1.5 > 1 ✓
• Converges

Watch out: ∑(1/(2n+1)^2) is NOT a p-series! Use comparison instead.

A - Alternating Series (Spot the (-1)^n)

Look for: Terms that alternate positive/negative

Three conditions must ALL be met:

1. b_n > 0 for all n
2. b_n is decreasing
3. lim(b_n) = 0 as n→∞

Example: ∑((-1)^n/n) (Alternating harmonic series)

• b_n = 1/n > 0 ✓
• 1/(n+1) < 1/n ✓ (decreasing)
• lim(1/n) = 0 ✓
• Converges! (Even though ∑(1/n) diverges)

R - Ratio Test (Perfect for Factorials)

Look for: Factorials (n!), exponentials (a^n), or products

Method: L = lim |a_(n+1)/a_n| as n→∞

• L < 1 → Converges
• L > 1 → Diverges
• L = 1 → Inconclusive

Example: ∑(2^n/n!)

• a_n = 2^n/n!, a_(n+1) = 2^(n+1)/(n+1)!
• L = lim |2^(n+1)/(n+1)! · n!/2^n| = lim 2/(n+1) = 0 < 1
• Converges

T - Other Tests (When Previous Tests Fail)

This includes Root Test, Comparison Tests, and Integral Test for complex cases.

Real BC Exam Application

Let's work through a typical BC exam problem using GPART:

Problem: Determine if ∑(n^2 + 1)/(n^4 + 3n^2 + 1) converges or diverges.

GPART Analysis:

• G: No constant ratio → Not geometric
• P: Not 1/n^p form → Not p-series
• A: No (-1)^n terms → Not alternating
• R: No factorials → Ratio test not ideal
• T: Use Limit Comparison Test

Solution: Dominant terms suggest comparing to ∑(1/n^2)

• L = lim [(n^2 + 1)/(n^4 + 3n^2 + 1)] / [1/n^2] = 1 > 0
• Since ∑(1/n^2) converges (p-series, p=2>1) and L=1>0
• Original series converges

Taylor Series Made Simple

SERIES Pro also handles Taylor and Maclaurin series with built-in formulas for:

• e^x = 1 + x + x²/2! + x³/3! + ... (converges for all x)
• sin(x) = x - x³/3! + x⁵/5! - ... (converges for all x)
• ln(1+x) = x - x²/2 + x³/3 - ... (converges for |x| < 1)

Plus error bound calculations and radius of convergence methods.

Why This Systematic Approach Works

The GPART Method transforms series problems from guesswork into strategy. Students report:

• Faster problem solving (30% time savings on average)
• Higher accuracy (fewer incorrect test choices)
• Boosted confidence (no more exam panic on series questions)

Take Your BC Performance to the Next Level

Ready to master series with the systematic GPART approach? SERIES Pro puts this entire methodology on your TI-84 Plus CE calculator, with worked examples and step-by-step guidance for every test type.

Coming in 2025: SERIES Pro will be included in our complete AP Calculus BC Bundle featuring specialized programs for derivatives, integrals, parametric equations, and more. Get SERIES Pro now and receive the bundle at a discount when it launches.

🧭 Related Programs

• Calculus Formula Guide – basic derivatives and integrals.

• AP Calculus BC Bundle – includes SERIES Pro and future BC modules.

• Free TI-84 Starter Bundle – 5 essential programs to get started.

Have questions about series or the GPART method? Use the contact page - I love helping BC students succeed!

 

📈 Final Thoughts

If you’re studying for the AP Calculus BC exam (or college-level Calculus II), SERIES Pro gives you everything you need for the Series unit right on your TI-84 Plus CE.
It saves you time, builds confidence, and keeps you focused on understanding patterns instead of memorizing them.

→ Download SERIES Pro for TI-84 Plus CE today and make series simple.