Question
If $1+2+3+\ldots+k=325$, then find $1^3+2^3+3^3+\ldots+k^3$
✓
Answer
$\begin{aligned} & 1+2+3+\ldots+k=325 \\ & 1^3+2^3+3^3+\ldots+k^3=\sum_1^n n^3 \\ & =\left(\frac{n(n+1)}{2}\right)^2 \\ & =\left(\sum_1^n n\right)^2 \\ & \text { If } 1+2+3+\ldots+k=325 \\ & 1^3+2^3+3^3+\ldots+k^3=(325)^2 \\ & =105625\end{aligned}$
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