Question

Provide the Maclaurin series of ln(1 x) for n = _____.

A) ln(1 x)
B) x - x²/2
C) x - x²/2 + x³/3
D) x - x²/2 + x³/3 - x⁴/4

Answer 1

The Maclaurin series of ln(1+x) is given by x - x²/2 + x³/3 - x⁴/4 + ..., so the correct answer is D) x - x²/2 + x³/3 - x⁴/4.

Step-by-step explanation:

The student has asked for the Maclaurin series of ln(1+x). The Maclaurin series for ln(1+x), centered at 0, is defined for -1 < x ≤ 1 and is given by:

x - x²/2 + x³/3 - x⁴/4 + ...

This is an alternating series where the sign alternates with each term, and each term is x to the power of n, divided by n. Therefore, the correct answer for the series up to the fourth term is:

D) x - x²/2 + x³/3 - x⁴/4