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Calculus · Series-And-Sums

Sum k^2 for k = 1 to n

\sum_{k=1}^{n} k^{2}

Step by step

  1. \sum_{k=1}^{n} k^{2}

    Write the sum out.

  2. 1 + 4 + 9 + 16 + \cdots

    The first few terms.

  3. = \frac{n \left(n + 1\right) \left(2 n + 1\right)}{6}

    Closed form (a standard summation formula, provable by induction).

Reveal the answer
\frac{n \left(n + 1\right) \left(2 n + 1\right)}{6}