A Particular Result

Algebra Level 2

Let $S(n)=1+2+\cdots+n$ be the sum of the first $n$ natural numbers and $C(n)=1^3+2^3+\cdots+n^3$ the sum of the first $n$ cubes. Then, what is the value of $k$ in $C(n)=S^k(n)$ ?

None of the other answers

k=\displaystyle\frac{3}{2}

k=\sqrt{3}

k=3

k=2

1 solution

Tom Engelsman
Sep 8, 2018

For all $n \in \mathbb{N}$ :

$S(n) = \frac{n(n+1)}{2}$ and $C(n) = \frac{n^2 (n+1)^2}{4}$

Hence, $C(n) = S^{2}(n) \Rightarrow \boxed{k = 2}.$

A Particular Result

1 solution

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