Question Number 164477 by mathocean1 last updated on 17/Jan/22
$${Using}\:{the}\:{definition},\:{show}\:{that}\: \\ $$$${U}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{sin}\left({k}\right)}{{k}!}\:{is}\:{a}\:{sequence}\:{of}\:{Cauchy}. \\ $$