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Section Summation Formulas

These formulas are useful for computing Riemann Sums.

  1. \(\dsp \Sigma_{i=1}^{n} c = nc\) where \(c\) is any real number

  2. \(\dsp \Sigma_{i=1}^{n} i = \frac{n(n+1)}{2}\)

  3. \(\dsp \Sigma_{i=1}^{n} i^{2} = \frac{n(n+1)(2n+1)}{6}\)

  4. \(\dsp \Sigma_{i=1}^{n} i^{3} = [\frac{n(n+1)}{2}]^{2}\)

  5. \(\dsp \Sigma_{i=1}^{n} i^{4} = \frac{n(n+1)(2n+1)(3n^{2}+3n+1)}{30}\)

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