Question 25For a sequence $u_1,$ $u_2,$ $\ldots,$ define $\Delta^1(u_n)=u_{n+1}-u_n$ and, for all integers $k\gt1,$ $\Delta^k(u_n)=\Delta^1(\Delta^{k-1}(u_n)).$ If $u_n=n^3+n,$ then $\Delta^k(u_n)=0$ for all $n$if $k=1$if $k=2,$ but not if $k=1$if $k=3,$ but not if $k=2$if $k=4,$ but not if $k=3$for no value of $k$