Any polynomial sum can be decomposed: sum(p(k), k=1 to n) where p(k) is a polynomial of degree d can be evaluated by expanding p(k) as a linear combination of $k^0$, $k^1$, ..., $k^d$ and applying standard formulas to each term. For non-polynomial rational sums, use partial fractions. For sums like sum(k*2^k): use the AGP technique (S-2S method). For sums like sum(1/sqrt(k)+1/sqrt(k+1)): rationalize the denominator to create a telescoping form: $\frac{1}{sqrt(k}$+sqrt(k+1))=sqrt(k+1)-sqrt(k). This is a JEE favorite.