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Question Number 106272 by Muhsang S L last updated on 04/Aug/20

(√(1 + (√(5 +(√(11 + (√(19 + (√(29 + (√…))))))))))) = ?

$$\sqrt{\mathrm{1}\:+\:\sqrt{\mathrm{5}\:+\sqrt{\mathrm{11}\:+\:\sqrt{\mathrm{19}\:+\:\sqrt{\mathrm{29}\:+\:\sqrt{\ldots}}}}}}\:=\:? \\ $$

Commented by Her_Majesty last updated on 04/Aug/20

2

$$\mathrm{2} \\ $$

Answered by Dwaipayan Shikari last updated on 04/Aug/20

(√(1+3))=2  (√(1+(√(5+4))))=2  (√(1+(√(5+(√(11+5))))))=2  (√(1+(√(5+(√(11+(√(19+6))))))))=2  (√(1+(√(5+(√(11+(√(19+(√(29+(√7)))))))))))....=2  (√(1+(√(5+(√(11+(√(19+(√(29+.....))))))))))=2    But many possible answers

$$\sqrt{\mathrm{1}+\mathrm{3}}=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\mathrm{4}}}=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\sqrt{\mathrm{11}+\mathrm{5}}}}=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\sqrt{\mathrm{11}+\sqrt{\mathrm{19}+\mathrm{6}}}}}=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\sqrt{\mathrm{11}+\sqrt{\mathrm{19}+\sqrt{\mathrm{29}+\sqrt{\mathrm{7}}}}}}}....=\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{5}+\sqrt{\mathrm{11}+\sqrt{\mathrm{19}+\sqrt{\mathrm{29}+.....}}}}}=\mathrm{2} \\ $$$$ \\ $$$${But}\:{many}\:{possible}\:{answers} \\ $$

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