How to Use the Series Sum Calculator
This calculator computes the sum of five common series types using standard formulas. It's ideal for math students studying sequences and series, and works for arithmetic, geometric, and power series.
Series Formulas
Arithmetic: Sn = n/2 × (2a + (n−1)d). Geometric: Sn = a(rⁿ − 1)/(r−1), or n×a if r=1. Natural numbers: n(n+1)/2. Squares: n(n+1)(2n+1)/6. Cubes: [n(n+1)/2]².
Notes
For geometric series with a large common ratio and many terms, results can be very large. The number of terms n must be a positive integer. The common difference and ratio can be negative or fractional.
Frequently Asked Questions
Yes. A negative common difference creates a decreasing arithmetic series. All standard formulas still apply.
A negative ratio creates an alternating geometric series. The sum formula works for any r ≠ 1, including negative values.
1³ + 2³ + ⋯ + n³ = (1 + 2 + ⋯ + n)², a beautiful identity discovered in antiquity. It shows the cube sum always equals the square of the natural number sum.