Question Number 798 by 123456 last updated on 15/Mar/15
$$\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+\centerdot\centerdot\centerdot}}}} \\ $$
Answered by prakash jain last updated on 15/Mar/15
$$\mathrm{Ramanujan}'{s}\:\mathrm{Formula} \\ $$$${x}+\mathrm{1}=\sqrt{\mathrm{1}+{x}\sqrt{\mathrm{1}+\left({x}+\mathrm{1}\right)\sqrt{\mathrm{1}+\left({x}+\mathrm{2}\right)\sqrt{\mathrm{1}+…}}}} \\ $$$$\mathrm{For}\:{x}=\mathrm{2} \\ $$$$\mathrm{3}=\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+..}}}} \\ $$