MathDB
Sequence u built upon a function

Source: 1976 AHSME Problem 25

May 19, 2014
functionPascal's TriangleAMC

Problem Statement

For a sequence u1,u2,u_1,u_2\dots, define Δ1(un)=un+1un\Delta^1(u_n)=u_{n+1}-u_n and, for all integer k>1k>1, Δk(un)=Δ1(Δk1(un))\Delta^k(u_n)=\Delta^1(\Delta^{k-1}(u_n)). If un=n3+nu_n=n^3+n, then Δk(un)=0\Delta^k(u_n)=0 for all nn
<spanclass=latexbold>(A)</span>if k=1<span class='latex-bold'>(A) </span>\text{if }k=1\qquad
<spanclass=latexbold>(B)</span>if k=2, but not if k=1<span class='latex-bold'>(B) </span>\text{if }k=2,\text{ but not if }k=1\qquad
<spanclass=latexbold>(C)</span>if k=3, but not if k=2<span class='latex-bold'>(C) </span>\text{if }k=3,\text{ but not if }k=2\qquad
<spanclass=latexbold>(D)</span>if k=4, but not if k=3<span class='latex-bold'>(D) </span>\text{if }k=4,\text{ but not if }k=3\qquad
<spanclass=latexbold>(E)</span>for no value of k<span class='latex-bold'>(E) </span>\text{for no value of }k