1. The problem is to understand and solve questions related to series in further mathematics. 2. A series is the sum of the terms of a sequence. The most common types are arithmetic series and geometric series. 3. For an arithmetic series, the sum of the first $n$ terms is given by the formula $$S_n = \frac{n}{2}(2a + (n-1)d)$$ where $a$ is the first term and $d$ is the common difference. 4. For a geometric series, the sum of the first $n$ terms is $$S_n = a \frac{1-r^n}{1-r}$$ where $a$ is the first term and $r$ is the common ratio, $r \neq 1$. 5. Important rules include: - The series converges if the terms approach zero and the sum approaches a finite limit. - For infinite geometric series with $|r| < 1$, the sum to infinity is $$S_\infty = \frac{a}{1-r}$$. 6. To solve a series problem, identify the type of series, find $a$, $d$ or $r$, and apply the appropriate formula. 7. Example: Find the sum of the first 5 terms of the arithmetic series with $a=3$ and $d=2$. 8. Using the formula: $$S_5 = \frac{5}{2}(2 \times 3 + (5-1) \times 2) = \frac{5}{2}(6 + 8) = \frac{5}{2} \times 14 = 35$$. 9. Therefore, the sum of the first 5 terms is 35. 10. Practice with different series types and parameters to master series problems.