Series Sum کا حساب کیسے لگائیں
Series Sum کیا ہے؟
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.
فارمولا
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
مرحلہ وار گائیڈ
- 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
حل شدہ مثالیں
ان پٹ
1+2+3+...+100
نتیجہ
100×101/2 = 5050 (Gauss method)
ان پٹ
Arithmetic: a=1, d=2, n=10
نتیجہ
Sum = 10/2×(2+18) = 100
اکثر پوچھے جانے والے سوالات
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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