\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
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Let \((u_n)\) be the sequence defined by \(u_n=(-1)^n+\dfrac{1}{n+1}\) for \(n\ge 0\). Which statements are true?
\((u_n)\) is monotonic from some index \(n_0\) onward.
\((u_n)\) is not monotonic from any index onward.
\((u_n)\) oscillates indefinitely, so it cannot be monotonic.
\((u_n)\) is strictly increasing.
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