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Question Number 98286 by  M±th+et+s last updated on 12/Jun/20

justify:  lim_(x→+∞)  Σ_(k≥1) (((k−1)! sin(x−(π/2)k))/x^k )=(π/2)

$${justify}: \\ $$$$\underset{{x}\rightarrow+\infty} {{lim}}\:\underset{{k}\geqslant\mathrm{1}} {\sum}\frac{\left({k}−\mathrm{1}\right)!\:{sin}\left({x}−\frac{\pi}{\mathrm{2}}{k}\right)}{{x}^{{k}} }=\frac{\pi}{\mathrm{2}} \\ $$

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