1. The problem is to solve an expression or equation using series expansion. 2. Series expansion involves expressing a function as an infinite sum of terms calculated from the values of its derivatives at a single point. 3. The most common series expansion is the Taylor series, given by: $$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!} (x - a)^n$$ where $f^{(n)}(a)$ is the $n$th derivative of $f$ evaluated at $a$. 4. To solve using series expansion, first identify the function and the point $a$ around which to expand. 5. Calculate the derivatives of the function at $a$. 6. Substitute these derivatives into the Taylor series formula. 7. Simplify the terms to get the series expansion. 8. Use the series to approximate the function or solve the problem as needed. This method is useful for approximating functions that are difficult to solve directly.