Q71 / 180 · COMEDK 2014 · Mathematics

For a natural number $n$, which one is the correct statement?

  • Correct answer
    A
    $1^{3}+2^{3}+\ldots .+n^{3}=(1+2+\ldots . .+n)^{2}$
  • 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'.

Relevant Questions