Help me evaluate the infinite series of

\[\displaystyle 1 + \sqrt {2 + \sqrt[3] {3+ \sqrt[4] {4 + \sqrt[5] {5 +......}}}}\].

Help me evaluate the infinite series of

\[\displaystyle 1 + \sqrt {2 + \sqrt[3] {3+ \sqrt[4] {4 + \sqrt[5] {5 +......}}}}\].

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TopNewestThanks for all your suggestions. I will post it into a question. – Bryan Lee Shi Yang · 1 year, 11 months ago

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Then does your number have a symbol, I mean Greek symbol or anything? – Bryan Lee Shi Yang · 1 year, 11 months ago

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– Archit Boobna · 1 year, 11 months ago

Same method, but did it manually.Log in to reply

Awesome question! – John Young Staff · 1 year, 11 months ago

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please solve and post a nice solution to this – Ritam Baidya · 1 year, 11 months ago

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The only thing I know is that it is less than 3, because of an identity by Ramanujan.Since it is above 2.9, we can find a good approximation.I dont think a closed form exists. – Bogdan Simeonov · 1 year, 11 months ago

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Ramanujan maybe? – Krishna Ar · 1 year, 11 months ago

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I think that the answer is about 2.911 – Archit Boobna · 1 year, 11 months ago

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And also give full step solutions (as much as possible) , bcs. I haven't figured out yet! – Bryan Lee Shi Yang · 1 year, 11 months ago

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– Krishna Sharma · 1 year, 11 months ago

Wait....you changed the problem -_- I was working on the previous one :VLog in to reply

– Bryan Lee Shi Yang · 1 year, 11 months ago

Haha XDLog in to reply

I made an equation ((((x-1)^2-2)^3-3)^4-4)^4........=x which gives 2.911 – Archit Boobna · 1 year, 11 months ago

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Please enter the answer correct to 3 decimal places. – Bryan Lee Shi Yang · 1 year, 11 months ago

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