Math Fundamentals18 sections · 814 units
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Common Sum Formulas

Reference sheet

Here are the formulas you'll use most often:

∙\bullet Sum of first nn integers: ∑i=1ni=n(n+1)2\sum_{i=1}^{n} i = \frac{n(n+1)}{2}

∙\bullet Sum of first nn squares: ∑i=1ni2=n(n+1)(2n+1)6\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}

∙\bullet Sum of first nn cubes: ∑i=1ni3=(n(n+1)2)2\sum_{i=1}^{n} i^3 = \left(\frac{n(n+1)}{2}\right)^2

∙\bullet Geometric series: ∑i=0n−1ri=rn−1r−1\sum_{i=0}^{n-1} r^i = \frac{r^n - 1}{r - 1} for r≠1r \neq 1

∙\bullet Arithmetic series: ∑i=0n−1(a+id)=n(2a+(n−1)d)2\sum_{i=0}^{n-1} (a + id) = \frac{n(2a + (n-1)d)}{2}