गणित

श्रेणी बेरीज कॅल्क्युलेटर

Series Sum Calculator

First term (a)

सार्व फरक (d)

Number of terms (n)

What is Series Sum Calculator?

▾

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.

DigiCalcs delivers precision-engineered tools for engineers and STEM professionals.

सूत्र

▾

f(x)Arithmetic: Sₙ = n(a₁+aₙ)/2; Geometric: Sₙ = a₁(1−rⁿ)/(1−r); General: Σₙ₌₁^N aₙ

Variable Legend

▾

प्रतीक	नाव	एकक	वर्णन
a₁	first term	—	—
aₙ	last term	—	—
r	common ratio (geometric)	—	for geometric series
Sₙ	sum of first n terms	—	—

How to Series Sum Calculator

▾

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

▾

Example 1

Given:1+2+3+...+100

परिणाम:100×101/2 = 5050 (Gauss method)

Example 2

Given:Arithmetic: a=1, d=2, n=10

परिणाम:Sum = 10/2×(2+18) = 100

Real-World Applications

▾

🏗️

Financial calculations (loan amortization)

🔬

Physics (summations in mechanics)

📊

Statistics (cumulative probability)

🏥

Engineering (load distribution)

⚙️

Computer graphics (compound transformations)

Series Sum Formulas

▾

Series	Formula	Example (n=10)
1+2+...+n	n(n+1)/2	55
1²+2²+...+n²	n(n+1)(2n+1)/6	385
1³+2³+...+n³	[n(n+1)/2]²	3025
Arithmetic	n/2×(2a+(n-1)d	Varies

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.

References

›Series — Khan Academy

Deep Dive

Read the full guide on how to use this calculator effectively

अधिक वाचा →

Accuracy-checked

Reviewed October 2026

Our methodology

साप्ताहिक गणित टिप्स मिळवा

दर आठवड्याला कॅल्क्युलेटर टिपा मिळवणाऱ्या १२,०००+ सदस्यांमध्ये सामील व्हा.

🔒

१००% मोफत

कधीही नोंदणी नाही

✓

अचूक

सत्यापित सूत्रे

⚡

त्वरित

टाइप करताना निकाल

📱

मोबाइल तयार

सर्व डिव्हाइस