Kako izračunati Series Sum
Kaj je Series Sum?
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.
Formula
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
Navodila po korakih
- 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
Worked Examples
Vnos
1+2+3+...+100
Rezultat
100×101/2 = 5050 (Gauss method)
Vnos
Arithmetic: a=1, d=2, n=10
Rezultat
Sum = 10/2×(2+18) = 100
Frequently Asked Questions
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.
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