Answer
The value at $ n=41$ of this mathematical expression, “ ${{n}^{2}}-n+41$ ” is not a prime number.
Work Step by Step
Let us consider the expression:
${{S}_{n}}$: ${{n}^{2}}-n+41$
For $ n=41$,
$\begin{align}
& {{S}_{n}}={{n}^{2}}-n+41 \\
& {{S}_{n}}=n(n-1)+41 \\
& {{S}_{n}}=(41\times 40)+41 \\
& {{S}_{41}}=(41)(40+1) \\
& {{S}_{41}}={{41}^{2}} \\
\end{align}$
Since, the ${{S}_{41}}$ is a perfect square; hence it is not a prime number
Thus, in the figure, one can see that the domino is true until $ n=40$ but after that it does not follow; the second condition of mathematical induction does not follow and hence the domino at $ n=41$ does not fall, thereby breaking the sequence.
