Question Number 188657 by Ajetunmobi last updated on 04/Mar/23
Answered by Ajetunmobi last updated on 04/Mar/23
$${please}\:{solve}\:{with}\:{detail}\:{solution} \\ $$
Answered by witcher3 last updated on 05/Mar/23
$$\mathrm{U}_{\mathrm{n}+\mathrm{1}} −\mathrm{U}_{\mathrm{n}} =\sqrt{\mathrm{u}_{\mathrm{n}} +\mathrm{2}}−\sqrt{\mathrm{u}_{\mathrm{n}−\mathrm{1}} +\mathrm{2}} \\ $$$$=\frac{\mathrm{u}_{\mathrm{n}} −\mathrm{u}_{\mathrm{n}−\mathrm{1}} }{\:\sqrt{\mathrm{u}_{\mathrm{n}} +\mathrm{2}}+\sqrt{\mathrm{u}_{\mathrm{n}−\mathrm{1}} +\mathrm{2}}}... \\ $$
Answered by mehdee42 last updated on 05/Mar/23
$$\forall{n}\in\mathbb{N}\:,\:{u}_{{n}} =\mathrm{2}\:\Rightarrow\:\forall{i}\in\mathbb{N}\:;\:{u}_{{i}} −{u}_{{i}−\mathrm{1}} =\mathrm{0}\: \\ $$$$!!!? \\ $$