Question

The sum of all numbers between $100$ and $10,000$ which are of the form $n^3(n\in N)$ is equal to?

• A. $55216$
• B. $53261$
• C. $51261$
• D. None of these

Answer 1

The correct option is A $55216$

We have,

$100<n^3<10000$

${100}^{\frac{1}{3}}<n^3<{10000}^{\frac{1}{3}}$

$4.64<n<21.5$

So n goes from 5 to 21

So we have addtion $5^3+6^3+7^3+.............+{21}^3$

Total is $=55216$

Hence this is the answer