Sigma notation: Σ_{k=a}^{b} f(k) = f(a) + f(a+1) + ... + f(b). Common formulas: Σk = n(n+1)/2, Σk² = n(n+1)(2n+1)/6, Σk³ = [n(n+1)/2]². Telescoping, geometric, and arithmetic sums have closed forms.
How to Use
Set up the sum:
- Expression: Choose or enter f(k)
- Bounds: Lower and upper
- Output: Sum with all terms
Closed Forms
- Σk = n(n+1)/2
- Σk² = n(n+1)(2n+1)/6
- Σ2^k = 2^(n+1) − 1
- Σ1/k ≈ ln(n) + γ
Techniques
Telescoping: terms cancel. Splitting: break into known sums. Closed-form: use formulas. Approximation: integral test for large n.
Step-by-Step Instructions
- 1Select an expression.
- 2Set lower bound.
- 3Set upper bound.
- 4View each term.
- 5Check total sum.