Series Sum ની ગણતરી કેવી રીતે કરવી
Series Sum શું છે?
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.
સૂત્ર
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
પગલું દ્વારા પગલું માર્ગદર્શિકા
- 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
ઇનપુટ
1+2+3+...+100
પરિણામ
100×101/2 = 5050 (Gauss method)
ઇનપુટ
Arithmetic: a=1, d=2, n=10
પરિણામ
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.
ગણતરી માટે તૈયાર છો? મફત Series Sum કેલ્ક્યુલેટર અજમાવી જુઓ
તેને જાતે અજમાવી જુઓ →