Quick questions on Sigma notation and summation explained: H2 Mathematics Sequences and Series

The three results you must know:

H2 questions almost always want a fully factorised answer, and the reliable way to get there is to pull out the common factor before expanding the bracket. When you sum a polynomial, every standard result shares the factor $\tfrac{n(n+1)}{6}$ (or a multiple of it), so factor that out first and simplify only what remains inside the bracket. In the worked example, taking out $\tfrac{n(n+1)}{6}$ left the simple bracket $(2n + 1) + 6 = 2n + 7$. Resisting the urge to multiply everything out, and instead extracting the common factor early, both saves work and produces the tidy factorised form the marks are awarded for.

Evaluate $\displaystyle\sum_{r=1}^{n} (4r - 1)$. [2 marks]

Express $\displaystyle\sum_{r=5}^{n} r^2$ in terms of $n$. [3 marks]

Evaluate $\displaystyle\sum_{r=1}^{10} r^3$. [2 marks]