The infinite series expansion of $\log(1 + x)$ for $-1 < x < 1$ is given by:

$\log(1 + x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \cdots$

This is a well-known result and matches the form of answer (b):

$x - \frac{x^2}{2} + \frac{x^3}{3} - \cdots$

Thus, the correct option is (b).

Would you like a detailed explanation on how this series is derived or more about Taylor expansions?

Here are 5 related questions for further exploration:

1. How is the series expansion of $\log(1+x)$ derived using calculus?
2. What is the radius of convergence of the series for $\log(1+x)$?
3. How would the series change for $\log(1-x)$?
4. Can you find the series expansion of $\frac{1}{1+x}$?
5. How is this series related to the geometric series?

Tip: The series for functions like $\log(1 + x)$ can be derived from the integral of simpler functions like $\frac{1}{1 + x}$, making it a key technique in calculus!