Q71 / 180 · COMEDK 2014 · Mathematics
For a natural number $n$, which one is the correct statement?
- Correct answerA$1^{3}+2^{3}+\ldots .+n^{3}=(1+2+\ldots . .+n)^{2}$
- B$1^{3}+2^{3}+\ldots .+n^{3}>(1+2+\ldots . .+n)^{2}$
- C$1^{3}+2^{3}+\ldots .+n^{3} < (1+2+\ldots .+n)^{2}$
- D$1^{3}+2^{3}+\ldots .+n^{3} \neq(1+2+\ldots .+n)^{2}$
Solution
$1^{3}+2^{3}+\ldots .+n^{3}$
$$
=\left(\frac{n(n+1)}{2}\right)^{2}=(1+2+\ldots .+n)^{2}
$$
Hence, the correct answer is option: 'A'.