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 + 3k^2 + 2k) = [n(n+1)/2]^2 + 3n(n+1)(2n+1)/6 + 2n(n+1)/2. But it's faster to use the direct formula n(n+1)(n+2)(n+3)/4.