Series Calculator — Step-by-Step Solutions
The Series Calculator evaluates mathematical series by computing partial sums. It handles arithmetic sequences, geometric sequences, and custom series defined by a general term expression.
Enter the general term of your series, specify the variable, start index, and end index. The calculator evaluates each term and provides the partial sum along with individual term values.
Your calculations will appear here
How to Use the Series Calculator
- Enter the general term of the series as an expression (e.g. 1/n^2).
- Specify the index variable, start index, and end index.
- The calculator evaluates each term and computes the partial sum.
Formula and Theory
A series is the sum of terms in a sequence. A finite series has a definite number of terms and always has a sum. An infinite series may or may not converge to a finite value.
Common series include arithmetic series (constant difference between terms), geometric series (constant ratio between terms), and p-series (sum of 1/n^p). Convergence tests determine whether an infinite series has a finite sum.
Worked Examples
Example 1: Arithmetic series
Problem: Find the sum of 1 + 2 + 3 + ... + 100
Solution: S = n(n+1)/2 = 100 * 101 / 2
Answer: 5050
Example 2: Geometric series
Problem: Find the sum of 1 + 1/2 + 1/4 + 1/8 + ... + 1/512
Solution: a = 1, r = 1/2, n = 10. S = (1 - (1/2)^10) / (1 - 1/2)
Answer: 1.998046875
Frequently Asked Questions
What does it mean for a series to converge?
Does the harmonic series converge?
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