learn.howToCalculate
learn.whatIsHeading
Series sum calculators find the total of all terms in arithmetic, geometric, or special mathematical series. They have applications in finance (annuities), physics, and pure mathematics.
Công thức
Arithmetic: Sₙ = n(a₁+aₙ)/2; Geometric: Sₙ = a₁(1−rⁿ)/(1−r); General: Σₙ₌₁^N aₙ
- a₁
- first term
- aₙ
- last term
- r
- common ratio (geometric) — for geometric series
- Sₙ
- sum of first n terms
Hướng dẫn từng bước
- 1Arithmetic: Sₙ = n/2 × (2a + (n−1)d)
- 2Sum 1 to n: n(n+1)/2
- 3Sum of squares: n(n+1)(2n+1)/6
- 4Sum of cubes: [n(n+1)/2]²
Ví dụ có lời giải
đầu vào
1+2+3+...+100
Kết quả
100×101/2 = 5050 (Gauss method)
đầu vào
Arithmetic: a=1, d=2, n=10
Kết quả
Sum = 10/2×(2+18) = 100
Câu hỏi thường gặp
What is the difference between a sequence and a series?
Sequence: list of terms (1, 2, 3, ...). Series: sum of sequence terms (1+2+3+...).
How do I find the sum of integers from 1 to n?
Use the formula Sₙ = n(n+1)/2. For n=100: S = 100×101/2 = 5050.
What is sigma notation?
Σ notation compactly represents series sums: Σₙ₌₁^N aₙ means a₁ + a₂ + ... + aₙ.
Sẵn sàng để tính toán? Dùng thử Máy tính Series Sum miễn phí
Hãy tự mình thử →