Sequences & Series
Arithmetic and geometric progressions, telescoping sums and recurrences.
Problems
- An Arithmetico-Geometric Series
- A Linear Combination of Two Series
- Splitting into Two Geometric Series
- Sum of Cubes of a Geometric Series
- Two Geometric Series That Converge
- A Telescoping Product
- Telescoping Sum over a Quartic
- A Sum That Telescopes to a Cube
- Recovering a Sequence from Its Sums
- A Second Difference of Square Roots
- Circles Meeting a Fixed Line
- A Recurrence with a Hidden Invariant
- Doubling or Dividing by Three
- A Cubic Recurrence in Closed Form
- Two Coupled Sequences
- A Branching Integer Recurrence
- First and Last Three Terms
- Combining Two Sums
- A Periodic Trigonometric Sum
- Limit from a Weighted Sum of Squares
- An Alternating Sine Sum
- Absolute Values in an Arithmetic Sum
- A Recurrence Whose Series Converges
- A Telescoping Sum of Square Roots
- A Three-Term Product Recurrence
- A Series of Remainders
- A Sine Recursion That Settles
- A Sequence Defined by Factorial Sums
- A Telescoping Tangent Series
- A Nested Radical of Factorials
- A Sequence With Two Moves