Question:
If $\sum_{r=1}^{n} r=55$, find $\sum_{r=1}^{n} r^{3} .$
Solution:
$\sum_{r=1}^{n} r^{3}=1^{3}+2^{3}+3^{3}+\ldots+n^{3}$
$=\left[\frac{n(n+1)}{2}\right]^{2}$
$=\left[\sum_{r=1}^{n} r\right]^{2}$
$=[55]^{2}$
$=3025$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.