Question Number 106272 by Muhsang S L last updated on 04/Aug/20
$$\sqrt{\mathrm{1}\:+\:\sqrt{\mathrm{5}\:+\sqrt{\mathrm{11}\:+\:\sqrt{\mathrm{19}\:+\:\sqrt{\mathrm{29}\:+\:\sqrt{\ldots}}}}}}\:=\:? \\ $$
Commented by Her_Majesty last updated on 04/Aug/20
$$\mathrm{2} \\ $$
Answered by Dwaipayan Shikari last updated on 04/Aug/20
$$\sqrt{\mathrm{1}+\mathrm{3}}=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\mathrm{4}}}=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\sqrt{\mathrm{11}+\mathrm{5}}}}=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\sqrt{\mathrm{11}+\sqrt{\mathrm{19}+\mathrm{6}}}}}=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\sqrt{\mathrm{11}+\sqrt{\mathrm{19}+\sqrt{\mathrm{29}+\sqrt{\mathrm{7}}}}}}}….=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\sqrt{\mathrm{11}+\sqrt{\mathrm{19}+\sqrt{\mathrm{29}+…..}}}}}=\mathrm{2} \\ $$$$ \\ $$$${But}\:{many}\:{possible}\:{answers} \\ $$