Question Number 184994 by Ml last updated on 15/Jan/23
$$\sqrt{\mathrm{1}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+....+\sqrt{\mathrm{70}}}}}}=? \\ $$
Commented by Frix last updated on 15/Jan/23
$$\mathrm{Use}\:\mathrm{a}\:\mathrm{calculator}. \\ $$$$\mathrm{Do}\:\mathrm{you}\:\mathrm{think}\:\sqrt{...+\sqrt{\mathrm{70}}}\:\mathrm{is}\:\mathrm{more}\:\mathrm{special}\:\mathrm{than} \\ $$$$\sqrt{...+\sqrt{\mathrm{71}}}\:\mathrm{or}\:\sqrt{...+\sqrt{\mathrm{69}}}?\:\mathrm{In}\:\mathrm{fact}\:\mathrm{the}\:\mathrm{only}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{interest}\:\mathrm{is}\:\sqrt{\mathrm{1}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+...}}}}\:\mathrm{to}\:\mathrm{infinity}. \\ $$