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

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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestThanks for all your suggestions. I will post it into a question. – Bryan Lee Shi Yang · 2 years, 5 months ago

Log in to reply

Then does your number have a symbol, I mean Greek symbol or anything? – Bryan Lee Shi Yang · 2 years, 5 months ago

Log in to reply

Using \(12\) or above to starts iteration gives equal amount precision, about \(50\) digits. – Damiann Mangan · 2 years, 5 months ago

Log in to reply

– Archit Boobna · 2 years, 5 months ago

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

Awesome question! – John Young Staff · 2 years, 5 months ago

Log in to reply

please solve and post a nice solution to this – Ritam Baidya · 2 years, 5 months ago

Log in to reply

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 · 2 years, 5 months ago

Log in to reply

Ramanujan maybe? – Krishna Ar · 2 years, 5 months ago

Log in to reply

I think that the answer is about 2.911 – Archit Boobna · 2 years, 5 months ago

Log in to reply

And also give full step solutions (as much as possible) , bcs. I haven't figured out yet! – Bryan Lee Shi Yang · 2 years, 5 months ago

Log in to reply

– Krishna Sharma · 2 years, 5 months ago

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

– Bryan Lee Shi Yang · 2 years, 5 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 · 2 years, 5 months ago

Log in to reply

Please enter the answer correct to 3 decimal places. – Bryan Lee Shi Yang · 2 years, 5 months ago

Log in to reply