Please tell me how you would find the answer for the following,

\[\large{\sqrt { x+\sqrt { \frac { { x }^{ 2 } }{ 2 } +\sqrt { \frac { { x }^{ 3 } }{ 3 } +\sqrt { \frac { { x }^{ 4 } }{ 4 } +\cdots \cdots \cdots } } } } }\]

Please tell me how you would find the answer for the following,

\[\large{\sqrt { x+\sqrt { \frac { { x }^{ 2 } }{ 2 } +\sqrt { \frac { { x }^{ 3 } }{ 3 } +\sqrt { \frac { { x }^{ 4 } }{ 4 } +\cdots \cdots \cdots } } } } }\]

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TopNewestK – Gourav Khullar · 1 year, 7 months ago

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I'm trying to find some clue to the problem.

its graph looks approximately like a square root graph multiplied by some constant equal to about 1.3(on small enough scales it doesn't miss by a lot but when you got to numbers like \(10^7\) it will miss by a lot)

So its value isn't constant at all.

The problem is really interesting though :) – Hummus A · 1 year, 7 months ago

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– Lakshya Sinha · 1 year, 7 months ago

Thank you friend, but of you give me a graph it would be really good. Again thanks:-)Log in to reply

https://s3.amazonaws.com/grapher/exports/0untf59cxm.png

https://s3.amazonaws.com/grapher/exports/l8t7vxlikg.png

red is the graph of the problem

blue is the graph of \(1.3533\sqrt{x}\) – Hummus A · 1 year, 7 months ago

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It's ans is 1 – Gourav Khullar · 1 year, 7 months ago

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I got 800\831 – Gourav Khullar · 1 year, 7 months ago

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– Lakshya Sinha · 1 year, 7 months ago

Can you explain me how (the steps)Log in to reply

@Aditya Kumar – Lakshya Sinha · 1 year, 7 months ago

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@Ishan Singh is awesome at handling infinity. – Aditya Kumar · 1 year, 7 months ago

Give me a week. I'll try to come up with a method if it exists.Log in to reply

– Lakshya Sinha · 1 year, 7 months ago

Thanks but please do remember. and I don't have a solution it's just my brain that came up with.Log in to reply

– Ishan Singh · 1 year, 7 months ago

Do you have any reason to believe that the closed form exists in terms of elementary functions?Log in to reply

– Lakshya Sinha · 1 year, 7 months ago

I don't understand what you said but I believe this can be taken out in terms of x.Log in to reply

just like the integrals of a lot of functions,they exist,but we didn't name a function for them and the integral can't be expressed using the elementary functions we know(\(\sin,\cos,\tan,\ln,x^a....\)),so this problem may be technically solvable,but it won't be the usual "solving" it would be creating a new function,

correct me if i'm wrong because i just learned about these examples of problems about a week ago – Hummus A · 1 year, 7 months ago

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@Michael Mendrin please you may be able to help me with this. thanks – Lakshya Sinha · 1 year, 9 months ago

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solution? – Dev Sharma · 1 year, 10 months ago

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– Lakshya Sinha · 1 year, 10 months ago

No solution yet! Big bang is a test of FIITJEELog in to reply

@Otto Bretscher – Lakshya Sinha · 1 year, 11 months ago

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@Chew-Seong Cheong , @Tanishq Varshney , @Sharky Kesa , @shivamani patil , @Pranjal Prashant , @Pranjal Jain, @Calvin Lin , @Utsav Bhardwaj . – Lakshya Sinha · 1 year, 11 months ago

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– Nihar Mahajan · 1 year, 11 months ago

Please limit your tags to at most 5 people.Log in to reply

– Kaustubh Miglani · 1 year, 11 months ago

hey buddy answer key of big bang is out.how much are u getting not too good here 793/831Log in to reply

– Dev Sharma · 1 year, 10 months ago

whats big bang here??Log in to reply

– Lakshya Sinha · 1 year, 11 months ago

BEkar 727/831, Sari galti vhemistry itne sare nahi kiye.Log in to reply

– Kaustubh Miglani · 1 year, 11 months ago

no prob buddy i am gonna explode avec tension any idea if i am gonna come 1st or notLog in to reply

– Lakshya Sinha · 1 year, 11 months ago

I am thinking whether I will come in top 5 or not. see ya meet you tomorrowLog in to reply

– Kaustubh Miglani · 1 year, 11 months ago

please reply fastLog in to reply

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– Lakshya Sinha · 1 year, 7 months ago

The graph by hummus aLog in to reply

– Swapnil Das · 1 year, 7 months ago

Hmm…Log in to reply