Technique 1: Direct Formula If general term is a polynomial in k, decompose into sum($k^3$), sum($k^2$), sum(k), and constants. Example: sum k(k+1) = sum($k^{2+k}$) = n(n+1)$\frac{2n+1}{6}$ + n$\frac{n+1}{2}$.

Technique 2: Telescoping Write $t_k$ = f(k) - f(k+1). Sum collapses to f(1) - f(n+1). Use partial fractions: $\frac{1}{k(k+1}$) = 1/k - $\frac{1}{k+1}$. For products of 3 terms: $\frac{1}{k(k+1}$(k+2)) = $\frac{1}{2}$($\frac{1}{k(k+1}$) - $\frac{1}{(k+1}$(k+2))).

Technique 3: S - rS (AGP) For sum of (AP part)*(GP part): multiply by r, subtract, simplify. The AP component telescopes, leaving a GP.

Technique 4: Method of Differences When differences of terms form AP or GP: compute differences, identify pattern, find general term.

Technique 5: Vn Method $\frac{Factorial}{Product sums}$ For sum of kk!: use kk! = (k+1)! - k!. For sum of k(k+1)...(k+m): use the generalized formula.

Technique 6: Rationalization For $\frac{1}{sqrt(k}$+sqrt(k+1)): multiply by (sqrt(k+1)-sqrt(k)) to telescop.

Choice guide: Polynomial in k -> Technique 1. Fractions with products -> Technique 2. AP*GP -> Technique 3. Unknown pattern -> Technique 4. Square roots -> Technique 6.