FreeMathHelp.com's Summation Calculator

Evaluate Summations Step-by-Step

The tool below will walk you through calculating the summation of an expression. Just enter the expression to the right of the summation symbol (capital sigma, Σ) and then the appropriate ranges above and below the symbol, like the example provided.

Enter a summation to evaluate:

Type naturally or click ⌨ in the box to use the math keyboard. For sigma notation, use \sum_{i=1}^{n} or click the Σ button. Examples: \sum_{i=1}^{10} i, \sum_{k=1}^{n} k^2

\sum_{i=1}^{10} i

LaTeX:

How does it work?

Enter any summation and we'll help you compute the result using appropriate formulas and techniques. Enter your summation in the box above and click the button to submit. The calculator will identify the type of summation (finite sum, geometric series, telescoping series, etc.) and apply the appropriate formulas and techniques. You'll see each step of the calculation process. Don't rely on any one tool to do all the work for you, and always check your work for correctness!

This is a brand new feature to FreeMathHelp.com -- hope you find it as useful as we do.

Try evaluating:

\sum_{i=1}^{10} i (sum of first 10 integers)
\sum_{k=1}^{n} k^2 (sum of squares)
\sum_{i=0}^{5} 2^i (geometric series)
\sum_{n=1}^{\infty} \frac{1}{2^n} (infinite geometric series)
\sum_{k=1}^{100} (2k + 3) (linear sum)

Common Summation Formulas

Here's a quick reference of summation formulas this calculator uses:

Sum of first n integers: Σ(i=1 to n) i = n(n+1)/2
Sum of squares: Σ(i=1 to n) i² = n(n+1)(2n+1)/6
Sum of cubes: Σ(i=1 to n) i³ = [n(n+1)/2]²
Geometric series: Σ(i=0 to n) ar^i = a(1-r^(n+1))/(1-r)
Infinite geometric: Σ(i=0 to ∞) ar^i = a/(1-r) when |r| < 1

Tips for Using the Calculator