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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, 9 months ago

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K · 1 year, 5 months ago

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 :) · 1 year, 5 months ago

Thank you friend, but of you give me a graph it would be really good. Again thanks:-) · 1 year, 5 months ago

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 $$1.3533\sqrt{x}$$ · 1 year, 5 months ago

It's ans is 1 · 1 year, 5 months ago

I got 800\831 · 1 year, 5 months ago

Can you explain me how (the steps) · 1 year, 5 months ago

@Aditya Kumar · 1 year, 5 months ago

Give me a week. I'll try to come up with a method if it exists. @Ishan Singh is awesome at handling infinity. · 1 year, 5 months ago

Thanks but please do remember. and I don't have a solution it's just my brain that came up with. · 1 year, 5 months ago

Do you have any reason to believe that the closed form exists in terms of elementary functions? · 1 year, 5 months ago

I don't understand what you said but I believe this can be taken out in terms of x. · 1 year, 5 months ago

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 · 1 year, 5 months ago

@Michael Mendrin please you may be able to help me with this. thanks · 1 year, 7 months ago

solution? · 1 year, 8 months ago

No solution yet! Big bang is a test of FIITJEE · 1 year, 8 months ago

@Otto Bretscher · 1 year, 9 months ago

Please limit your tags to at most 5 people. · 1 year, 9 months ago

hey buddy answer key of big bang is out.how much are u getting not too good here 793/831 · 1 year, 9 months ago

whats big bang here?? · 1 year, 8 months ago

BEkar 727/831, Sari galti vhemistry itne sare nahi kiye. · 1 year, 9 months ago

no prob buddy i am gonna explode avec tension any idea if i am gonna come 1st or not · 1 year, 9 months ago

I am thinking whether I will come in top 5 or not. see ya meet you tomorrow · 1 year, 9 months ago

Comment deleted Mar 31, 2016

The graph by hummus a · 1 year, 5 months ago