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Calculus
Series & Sequences Cheat Sheet
Complete series and sequences cheat sheet with arithmetic, geometric, power series, Taylor series, and convergence tests. Free PDF download.
Arithmetic Sequences
| Name | Formula | Notes |
|---|---|---|
| nth Term | d = common difference | |
| Sum of n Terms | ||
| Sum Formula 2 | ||
| Common Difference |
Geometric Sequences
| Name | Formula | Notes |
|---|---|---|
| nth Term | r = common ratio | |
| Sum of n Terms | r ≠ 1 | |
| Infinite Sum | |r| < 1 for convergence | |
| Common Ratio |
Common Series
| Name | Formula | Notes |
|---|---|---|
| Sum of Integers | ||
| Sum of Squares | ||
| Sum of Cubes |
Power Series
| Name | Formula | Notes |
|---|---|---|
| General Form | a = center | |
| Exponential | ||
| Sine | ||
| Cosine | ||
| Geometric | |x| < 1 |
Taylor Series
| Name | Formula | Notes |
|---|---|---|
| Taylor Formula | ||
| Maclaurin (a=0) | ||
| ln(1+x) | -1 < x ≤ 1 |
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