Properties of summation:

• sum(c * $a_k$) = c * sum($a_k$) (constant factor)
• sum($a_k$ + $b_k$) = sum($a_k$) + sum($b_k$) (linearity)
• $sum_{k=1}^{n}$ c = nc (sum of a constant)
• $sum_{k=m}^{n}$ $a_k$ = $sum_{k=1}^{n}$ $a_k$ - $sum_{k=1}^{m-1}$ $a_k$ (splitting range)

Decomposition technique: Express the general term as a sum of standard forms: $t_k$ = $Ak^3$ + $Bk^2$ + Ck + D Then sum = Asum($k^3$) + Bsum($k^2$) + Csum(k) + Dn

Example: sum of k(k+1)(k+2) = sum($k^3$ + 3$k^2$ + 2k) = [n$\frac{n+1}{2}$]^2 + 3n(n+1)$\frac{2n+1}{6}$ + 2n$\frac{n+1}{2}$. But it's faster to use the direct formula n(n+1)(n+2)$\frac{n+3}{4}$.