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Question Number 107598 by mathDivergent last updated on 11/Aug/20
    Calculate:  (√(1 + (√(2 + (√(3 + (√(4 + (√(5 + ...))))))))))
$$\:\:\:\:\mathrm{Calculate}:\:\:\sqrt{\mathrm{1}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{3}\:+\:\sqrt{\mathrm{4}\:+\:\sqrt{\mathrm{5}\:+\:…}}}}} \\ $$
Commented by Her_Majesty last updated on 11/Aug/20
≈1.75793275662
$$\approx\mathrm{1}.\mathrm{75793275662} \\ $$
Commented by Dwaipayan Shikari last updated on 11/Aug/20
Sir , how can i get this?
$${Sir}\:,\:{how}\:{can}\:{i}\:{get}\:{this}? \\ $$
Commented by Her_Majesty last updated on 11/Aug/20
using a calculator and patience  I started with  100  99+(√(100))  98+(√(last answer))  ...  I don′t see any value dependent on e, π or  other known constants but I might be wrong  and please don′t say “Sir” as I′m a woman  no matter what you or others may think
$${using}\:{a}\:{calculator}\:{and}\:{patience} \\ $$$${I}\:{started}\:{with} \\ $$$$\mathrm{100} \\ $$$$\mathrm{99}+\sqrt{\mathrm{100}} \\ $$$$\mathrm{98}+\sqrt{{last}\:{answer}} \\ $$$$… \\ $$$${I}\:{don}'{t}\:{see}\:{any}\:{value}\:{dependent}\:{on}\:{e},\:\pi\:{or} \\ $$$${other}\:{known}\:{constants}\:{but}\:{I}\:{might}\:{be}\:{wrong} \\ $$$${and}\:{please}\:{don}'{t}\:{say}\:“{Sir}''\:{as}\:{I}'{m}\:{a}\:{woman} \\ $$$${no}\:{matter}\:{what}\:{you}\:{or}\:{others}\:{may}\:{think} \\ $$

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