1976 AHSME Problems/Problem 25

Problem

For a sequence $u_1,u_2\dots$ , define $\Delta^1(u_n)=u_{n+1}-u_n$ and, for all integer $k>1, \Delta^k(u_n)=\Delta^1(\Delta^{k-1}(u_n))$ . If $u_n=n^3+n$ , then $\Delta^k(u_n)=0$ for all $n$

$\textbf{(A) }\text{if }k=1\qquad \\ \textbf{(B) }\text{if }k=2,\text{ but not if }k=1\qquad \\ \textbf{(C) }\text{if }k=3,\text{ but not if }k=2\qquad \\ \textbf{(D) }\text{if }k=4,\text{ but not if }k=3\qquad\\ \textbf{(E) }\text{for no value of }k$

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1976 AHSME Problems/Problem 25

Problem