Infinite Series - Complete Interactive Lesson
Part 1: Partial Sums & Geometric Series
Infinite Series
Part 1 of 7 — Partial Sums & Geometric Series
Partial Sums
means .
Geometric Series
Diverges if .
Example
Geometric Series 🎯
Key Takeaways — Part 1
Geometric: when . First ratio, then answer!
Part 2: Telescoping Series & Divergence Test
Infinite Series
Part 2 of 7 — Telescoping Series & Divergence Test
Telescoping Series
sum_{n=1}^{infty}left(\frac{1}{n} - \frac{1}{n+1}\right) = 1
Partial sum: .
Part 3: Integral Test & p-Series
Infinite Series
Part 3 of 7 — Integral Test & -Series
Integral Test
If is positive, continuous, decreasing for , and :
Part 4: Comparison Tests
Infinite Series
Part 4 of 7 — Comparison Tests
Direct Comparison Test
For :
- converges → converges
Part 5: Ratio & Root Tests
Infinite Series
Part 5 of 7 — Ratio & Root Tests
Ratio Test
L = lim_{n \to infty} left|\frac{a_{n+1}}{a_n}\right|
- : converges absolutely
- (or ): diverges
- : inconclusive
Part 6: Practice Workshop
Infinite Series
Part 6 of 7 — Practice Workshop
Mixed Series Practice 🎯
Workshop Complete!
Part 7: Final Assessment
Infinite Series — Review
Part 7 of 7 — Final Assessment
Final Assessment 🎯