Track / Stage 4 / 182 of 340 #442 of 2000

Problem 442

AMC 12 late, AIME early

Algebra Difficulty 4.8 Find the answer

[Summation of numerical sequences and series of differences]

Output the formula for the sum $1^{3}+2^{3}+3^{3}+\ldots+n^{3}$ .

Your answer

Official solution

Find the sequence $a_{\mathrm{n}}$ of the form $a_{n}=A n^{4}+B n^{3}+C n^{2}+D n$ , for which $\Delta a_{n}=n^{3}$ .

## Answer

$\left(\frac{n(n+1)}{2}\right)^{2}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.