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