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Sigma Notation
Sigma Notation Calculator
Evaluate summation expressions written in sigma (Σ) notation.
Expression Type
Linear (ak + b)
Quadratic (ak² + b)
Power (k^n)
Factorial (1/k!)
Lower (k =)
Upper (k =)
Coefficient (a)
Constant (b)
Expanded Form
Common Sigma Formulas
Σk = n(n+1)/2
Sum of first n integers
Σk² = n(n+1)(2n+1)/6
Sum of squares
Σk³ = [n(n+1)/2]²
Sum of cubes
Σr^k = (1-r^n)/(1-r)
Geometric sum
Σ1/k! → e
Approaches e ≈ 2.718
Σ(-1)^k/k → -ln(2)
Alternating harmonic
Related Calculators
Sequence Sum
Partial Sum
Infinite Series
Arithmetic Sequence