Question

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
• B. (2) only
• C. Both (1) and (2)
• D. Neither (1) nor (2)

Answer 1

The correct option is B (2) only

Sum of cubes of first $n$ consecutive natural numbers is given by ${\left(\frac{n(n+1)}{2}\right)}^2$
Putting $n=20,$ we have sum $={\left(\frac{20(20+1)}{2}\right)}^2=44100$

Sum of squares of first $n$ consecutive natural numbers is given by $\frac{n(n+1)(2n+1)}{6}$
Putting $n=20,$ we have the sum$=\frac{20(20+1)(2\times 20+1)}{6}=2870$
Hence, option B is correct