How does the Series Sum Calculator work?

Arithmetic: Sₙ = n/2 × (2a + (n−1)d) Then: Sum 1 to n: n(n+1)/2 Then: Sum of squares: n(n+1)(2n+1)/6 Then: Sum of cubes: [n(n+1)/2]².

Can you give an example of how to use the Series Sum Calculator?

Example: Input 1+2+3+...+100 gives a result of 100×101/2 = 5050 (Gauss method).

Is the Series Sum Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Series Sum Calculator?

Our Series Sum Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Series Sum Calculator

First term (a)

Common diff (d)

Number of terms (n)

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.

Symbol	Name	Unit	Description
a₁	first term	—	—
aₙ	last term	—	—
r	common ratio (geometric)	—	for geometric series
Sₙ	sum of first n terms	—	—

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

References

›Series — Khan Academy

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