Q153 / 270 · NDA 2012 (Phase 2) · Mathematics

Consider the following statements : 1. The sum of cubes of first 20 natural numbers is 44400. 2. The sum of squares of first 20 natural numbers is 2870. Which of the above statements is/are correct?

  • A
    $1$ only
  • Correct answer
    B
    $2$ only
  • C
    Both $1$ and $2$
  • D
    Neither $1$ nor $2$

Solution

$\because \quad 1^3+2^3+3^3+\ldots \ldots+n^3=\left(\frac{n(n+1)}{2}\right)^2$ $\therefore 1^3+2^3+3^3+\ldots \ldots .+20^3=\left(\frac{20.21}{2}\right)^2$ $=(10 \times 21)^2=44100$ $1^2+2^2+3^3+\ldots \ldots+n^2=\frac{1}{6} n(n+1)(2 n+1)$ $\therefore \quad 1^2+2^2+\ldots \ldots+20^2=\frac{1}{6} 20.21 .41=2870$

Hence, the correct answer is option: 'B'.

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