Kalkulator Sigma / Penjumlahan

Evaluasi notasi Σ (sigma) dan visualisasikan setiap suku serta jumlah kumulatif dengan diagram batang interaktif.

Σ Term Visualization
Σ
Enter expression and bounds, then compute Σ to see the chart.

Try these examples

Arithmetic
Σ i (1→n)
Sum of natural numbers
Squares
Σ i² (1→n)
Sum of squares
Harmonic
Σ 1/i (1→n)
Harmonic series
Geometric
Σ 2ⁱ (1→n)
Geometric series
📚 Sigma Notation

Understanding Σ (Sigma) Notation

Sigma notation (Σ) is a compact way to write the sum of a sequence of terms. Instead of writing out every term, you define a pattern and specify where to start and stop.

Σᵢ₌ₐⁿ f(i) = f(a) + f(a+1) + f(a+2) + ... + f(n)

Common useful formulas:

  • Σᵢ₌₁ⁿ i = n(n+1)/2 — Sum of first n natural numbers
  • Σᵢ₌₁ⁿ i² = n(n+1)(2n+1)/6 — Sum of squares
  • Σᵢ₌₁ⁿ i³ = [n(n+1)/2]² — Sum of cubes
  • Σᵢ₌₀ⁿ rⁱ = (1 - rⁿ⁺¹)/(1 - r) — Geometric series
❓ FAQ

Frequently Asked Questions

Yes! The calculator automatically converts n to i internally. You can write n^2 or n*(n+1) and it will work correctly.
For performance, keep the number of terms under 500. For larger sums (e.g., 1 to 10,000), consider using the closed-form formula instead of brute-force summation.