Constant "\(1\)" sum
\[\sum_{r=1}^{n} 1 = n\]
Fundamental A. P.
\[\sum_{r=1}^{n} r = \frac{n}{2}(n+1)\]
Sum of squares of consecutive integers
\[\sum_{r=1}^{n} r^2 = \frac{n}{6}(2n+1)(n+1)\]
Sum of cubes of consecutive integers
\[\sum_{r=1}^{n} r^3 = \frac{n^2}{4}(n+1)^2\]
Fundamental G.P. (Geometric Progression)
\[\sum_{r=1}^{n} R^{r-1} = \frac{R^n - 1}{R - 1} \quad (R \neq 1)\]
Note: We will formally introduce the Geometric Progression in the next unit.

\[\sum_{r=1}^{n} r^2 = \frac{n}{6}(2n+1)(n+1)\]

\[\sum_{r=1}^{n} r^3 = \frac{n^2}{4}(n+1)^2\]

\[\sum_{r=1}^{n} R^{r-1} = \frac{R^n - 1}{R - 1} \quad (R \neq 1)\]

Note: We will formally introduce the Geometric Progression in the next unit.

Sigma Notation

Recurrence Relations and Summation

International Baccalaureate Higher Level Mathematics

Summary of summation formulae

Summary of summation formulae