Q. For any odd integer$\ n \geq 1,\ n^{3} - (n - 1)^{3} + ... + ( - 1)^{n - 1}1^{3}$ is equal to
A) $\frac{1}{2}(n - 1)^{2}(2n - 1)$
B) $\frac{1}{4}(n - 1)^{2}(2n - 1)$
C) $\frac{1}{2}(n + 1)^{2}(2n - 1)$
D) $\frac{1}{4}(n + 1)^{2}(2n - 1)$
Explanation
The correct answer is Option D: $\frac{1}{4}(n + 1)^{2}(2n - 1)$.
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.