Sum Calculator

Use the index variable, e.g. i^2, 1/i, 2^i, (2i-1), sin(i).
Increment applied to the index each term.
Result
385
Summation (Sigma Notation) Calculator
Number of terms
10
Expanded form
1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100
Notation
Σ(i = 1 to 10) i^2
Closed form used to check the answer
sum_{i=1}^{n} i^2 = n(n+1)(2n+1)/6, evaluated as P(10) - P(0) = 385
Smallest term
1
Largest term
100
Worked out from NIST Digital Library of Mathematical Functions, section 26.1 (sums of powers, geometric series) and 1 other source.

How this is worked out

4 steps
  1. Σ(i = 1 to 10) i^2 has 10 terms.
  2. Terms: 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100
  3. Closed form check: sum_{i=1}^{n} i^2 = n(n+1)(2n+1)/6, evaluated as P(10) - P(0) = 385.
  4. Total = 385.
Termstable
1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Results are general information, not financial, tax, legal, medical or engineering advice.