কীভাবে Series Sum গণনা করবেন
Series Sum কি?
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.
সূত্র
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
ধাপে ধাপে নির্দেশিকা
- 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
সমাধান করা উদাহরণ
ইনপুট
1+2+3+...+100
ফলাফল
100×101/2 = 5050 (Gauss method)
ইনপুট
Arithmetic: a=1, d=2, n=10
ফলাফল
Sum = 10/2×(2+18) = 100
সচরাচর জিজ্ঞাসা
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.
গণনা করতে প্রস্তুত? বিনামূল্যে Series Sum ক্যালকুলেটর চেষ্টা করুন
নিজে চেষ্টা করে দেখুন →