Series Summation
Sum of arithmetic, geometric, and custom term formula series.
Arithmetic series: first term a₁, common difference d, number of terms n
Common Summation Formulas
- Arithmetic Series：Sₙ = n(a₁+aₙ)/2 = na₁ + n(n-1)d/2
- Geometric Series：Sₙ = a₁(1-qⁿ)/(1-q) (q≠1)
- Sum of Natural Numbers：1+2+...+n = n(n+1)/2
- Sum of Squares：1²+2²+...+n² = n(n+1)(2n+1)/6
- Sum of Cubes：1³+2³+...+n³ = [n(n+1)/2]²
Usage Instructions
Features
Series summation tool supporting arithmetic and geometric series, as well as custom term formulas, automatically displaying the last term, sum, and the first several terms.
Steps
Select a tab (Arithmetic/Geometric/Custom) → enter the first term, common difference/ratio, and number of terms (or start, end, and term formula) → automatically or click "Calculate" to view the last term, sum, and sequence.
Notes
All computations run locally in the browser; custom sum range must not exceed 100000; the term formula uses i as the variable and supports arithmetic and exponentiation.