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math.sum-of-squares Calculator
Calculates the sum of squares of integers 1 to n (n(n+1)(2n+1)/6) and the sum of cubes (n²(n+1)²/4). These closed-form summation formulas are proved by mathematical induction and appear in Riemann sum derivations and statistical calculations.
Inputs
N
Reference formula or conversion factor shown for context.
Results
Σk² (sum of squares)
The arithmetic total of all input values.
Σk (sum of 1 to n)
The arithmetic total of all input values.
Σk³ (sum of cubes)
The arithmetic total of all input values.
Σk² = n(n+1)(2n+1)/6
Sample size or count used in the calculation.
Σk³ = [n(n+1)/2]²
Sample size or count used in the calculation.
note
Supplementary information explaining an assumption, caveat, or important context for interpreting the result.