Series Sum ಅನ್ನು ಹೇಗೆ ಲೆಕ್ಕ ಹಾಕುವುದು
Series Sum ಎಂದರೇನು?
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.
ಸೂತ್ರ
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
ಹಂತ-ಹಂತದ ಮಾರ್ಗದರ್ಶಿ
- 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
ಇನ್ಪುಟ್
1+2+3+...+100
ಫಲಿತಾಂಶ
100×101/2 = 5050 (Gauss method)
ಇನ್ಪುಟ್
Arithmetic: a=1, d=2, n=10
ಫಲಿತಾಂಶ
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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