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Such infinite roots

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

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

Note by Lakshya Sinha
1 year, 3 months ago

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K Gourav Khullar · 11 months, 1 week 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 · 11 months, 1 week ago

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@Hummus A Thank you friend, but of you give me a graph it would be really good. Again thanks:-) Lakshya Sinha · 11 months, 1 week ago

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@Lakshya Sinha https://s3.amazonaws.com/grapher/exports/tupibgzrxn.png

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 · 11 months, 1 week ago

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It's ans is 1 Gourav Khullar · 11 months, 1 week ago

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I got 800\831 Gourav Khullar · 11 months, 1 week ago

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@Gourav Khullar Can you explain me how (the steps) Lakshya Sinha · 11 months, 1 week ago

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@Aditya Kumar Lakshya Sinha · 11 months, 2 weeks ago

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@Lakshya Sinha Give me a week. I'll try to come up with a method if it exists. @Ishan Singh is awesome at handling infinity. Aditya Kumar · 11 months, 2 weeks ago

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@Aditya Kumar Thanks but please do remember. and I don't have a solution it's just my brain that came up with. Lakshya Sinha · 11 months, 2 weeks ago

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@Lakshya Sinha Do you have any reason to believe that the closed form exists in terms of elementary functions? Ishan Singh · 11 months, 1 week ago

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@Ishan Singh I don't understand what you said but I believe this can be taken out in terms of x. Lakshya Sinha · 11 months, 1 week ago

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@Lakshya Sinha if i'm right i think @Ishan Singh is meaning this

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 · 11 months, 1 week ago

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

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solution? Dev Sharma · 1 year, 2 months ago

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@Dev Sharma No solution yet! Big bang is a test of FIITJEE Lakshya Sinha · 1 year, 2 months ago

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@Otto Bretscher Lakshya Sinha · 1 year, 3 months ago

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@Lakshya Sinha Please limit your tags to at most 5 people. Nihar Mahajan · 1 year, 3 months ago

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@Lakshya Sinha hey buddy answer key of big bang is out.how much are u getting not too good here 793/831 Kaustubh Miglani · 1 year, 3 months ago

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@Kaustubh Miglani whats big bang here?? Dev Sharma · 1 year, 2 months ago

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@Kaustubh Miglani BEkar 727/831, Sari galti vhemistry itne sare nahi kiye. Lakshya Sinha · 1 year, 3 months ago

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@Lakshya Sinha no prob buddy i am gonna explode avec tension any idea if i am gonna come 1st or not Kaustubh Miglani · 1 year, 3 months ago

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@Kaustubh Miglani I am thinking whether I will come in top 5 or not. see ya meet you tomorrow Lakshya Sinha · 1 year, 3 months ago

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@Kaustubh Miglani please reply fast Kaustubh Miglani · 1 year, 3 months ago

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Comment deleted 9 months ago

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@Swapnil Das The graph by hummus a Lakshya Sinha · 11 months ago

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@Lakshya Sinha Hmm… Swapnil Das · 11 months ago

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