Question Detail
Question
The nth term of the Maclaurin series expansion of cos 3x is
Correct Answer
Option D is the correct answer.
Detailed Explanation
The Maclaurin series for cos(u) is given by the sum Σ (from n=0 to ∞) [(-1)ⁿ * u^(2n)] / (2n)!. For cos(3x), substitute u=3x into this formula. The nth term is therefore [(-1)ⁿ * (3x)²ⁿ] / (2n)!. Option D correctly represents this term.
Hint
Recall the standard Maclaurin series for cos(u) and substitute u with 3x. The general term for cos(u) involves even powers and factorials.