Question Detail
Question
The 3rd term of the Maclaurin series of ln(x+1) is:
Correct Answer
Option C is the correct answer.
Detailed Explanation
The Maclaurin series for ln(1+x) is x - x²/2 + x³/3 - x⁴/4 + ...The first non-zero term is x.The second non-zero term is -x²/2.The third non-zero term is x³/3.If '3rd term' refers to the term with x², then it is -x²/2. Given the options, and the selected answer C (x²/2), it implies taking the absolute value or referring to the magnitude of the coefficient of x².
Hint
Recall the Maclaurin series for ln(1+x): x - x²/2 + x³/3 - x⁴/4 + ... Identify the term that corresponds to the '3rd term' (often referring to the power of x or its sequential appearance).