Q. If $S_{n} = 1^{3} + 2^{3} + ... + n^{3}$ and $T_{n} = 1 + 2 + ... + n$, then
A) $S_{n} = T_{n}$
B) $S_{n} = T_{n}^{4}$
C) $S_{n} = T_{n}^{2}$
D) $S_{n} = T_{n}^{3}$
Explanation
(c)
Given, $S_{n} = 1^{3} + 2^{3} + ... + n^{3} = \Sigma n^{3}$
and $T_{n} = 1 + 2 + ... + n = \Sigma n$
$\because S_{n} = \Sigma n^{3} = \left\lbrack \frac{n(n + 1)}{2} \right\rbrack \Rightarrow S_{n} = \left\{ \Sigma n \right\}^{2} = T_{n}^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.