Summation notation Σ compactly expresses adding a series of terms. Σᵢ₌₁ⁿ i = 1+2+3+...+n = n(n+1)/2. This tool computes sums for arithmetic series (constant difference), geometric series (constant ratio), power sums (Σi², Σi³), and custom expressions.
How to Use
Set up your summation:
- Type: Arithmetic, geometric, or power
- Range: Start and end values
- Parameters: First term, common difference/ratio
Closed-Form Formulas
- Σi = n(n+1)/2
- Σi² = n(n+1)(2n+1)/6
- Σi³ = [n(n+1)/2]²
- Σar^i = a(1−rⁿ)/(1−r)
Applications
- Statistics: mean = Σxᵢ/n
- Physics: total distance, work
- Finance: annuity payments
- CS: algorithm complexity analysis
Step-by-Step Instructions
- 1Select series type.
- 2Set the start and end index.
- 3Enter parameters (first term, difference/ratio).
- 4View the sum and each term.
- 5Check the closed-form formula.