For a nonnegative real number \(x\), let \[ f_n(x)=\frac{\prod_{k=1}^{n-1} ((x+k)(x+k+1))}{ (n!)^2}\] for a positive integer \(n\). Determine \(\lim_{n\to\infty}f_n(x)\).
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2014-22 Limit,
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This sequence does not converge. I think the problem needs some correction.
@JKJ I don’t think so. It is not obvious that the sequence diverges for all x.