Which one of the following is the difference of the sum of cubes of first ten natural numbers and the sum of squares of first ten natural numbers?
[amp_mcq option1=”2400″ option2=”2640″ option3=”2880″ option4=”2000″ correct=”option2″]
This question was previously asked in
UPSC CAPF – 2022
The sum of the first ten natural numbers’ cubes is calculated using the formula $[\frac{n(n+1)}{2}]^2$ with n=10, giving $[\frac{10(11)}{2}]^2 = 55^2 = 3025$. The sum of the first ten natural numbers’ squares is calculated using the formula $\frac{n(n+1)(2n+1)}{6}$ with n=10, giving $\frac{10(11)(21)}{6} = \frac{2310}{6} = 385$. The difference is $3025 – 385 = 2640$.
The problem requires knowing the formulas for the sum of cubes and the sum of squares of the first ‘n’ natural numbers and applying them for n=10.