iran-konkur 2015 Q143

iran-konkur · Other · konkur-riazi_1394 Proof by induction Prove a summation inequality by induction
143- In proving the inequality $3^{n+1} > n!$ by mathematical induction, after finding a suitable number $m$, the inductive step relation for $k \geq m$ is which of the following?
(1) $k+1 > 2,\ m = 5$(2) $k+1 > 2,\ m = 6$
(3) $(2k+1) > 4,\ m = 5$(4) $(2k+1) > 4,\ m = 6$

\textbf{143-} In proving the inequality $3^{n+1} > n!$ by mathematical induction, after finding a suitable number $m$, the inductive step relation for $k \geq m$ is which of the following?

\begin{tabular}{ll}
(1) $k+1 > 2,\ m = 5$ & (2) $k+1 > 2,\ m = 6$ \\
(3) $(2k+1) > 4,\ m = 5$ & (4) $(2k+1) > 4,\ m = 6$
\end{tabular}

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