Such infinite roots

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

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

#Algebra #Calculus #Summation #SummationOfSeries

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Gourav Khullar - 5 years, 4 months ago

@Chew-Seong Cheong , @Tanishq Varshney , @Sharky Kesa , @shivamani patil , @Pranjal Prashant , @Pranjal Jain, @Calvin Lin , @Utsav Bhardwaj .

Department 8 - 5 years, 8 months ago

Please limit your tags to at most 5 people.

Nihar Mahajan - 5 years, 8 months ago

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

Kaustubh Miglani - 5 years, 8 months ago

please reply fast

Kaustubh Miglani - 5 years, 8 months ago

BEkar 727/831, Sari galti vhemistry itne sare nahi kiye.

Department 8 - 5 years, 8 months ago

@Department 8 – no prob buddy i am gonna explode avec tension any idea if i am gonna come 1st or not

Kaustubh Miglani - 5 years, 8 months ago

@Kaustubh Miglani – I am thinking whether I will come in top 5 or not. see ya meet you tomorrow

Department 8 - 5 years, 8 months ago

whats big bang here??

Dev Sharma - 5 years, 7 months ago

@Otto Bretscher

Department 8 - 5 years, 8 months ago

solution?

Dev Sharma - 5 years, 7 months ago

No solution yet! Big bang is a test of FIITJEE

Department 8 - 5 years, 7 months ago

@Michael Mendrin please you may be able to help me with this. thanks

Department 8 - 5 years, 6 months ago

@Aditya Kumar

Department 8 - 5 years, 4 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.

Aditya Kumar - 5 years, 4 months ago

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

Department 8 - 5 years, 4 months ago

@Department 8 – Do you have any reason to believe that the closed form exists in terms of elementary functions?

Ishan Singh - 5 years, 4 months ago

@Ishan Singh – I don't understand what you said but I believe this can be taken out in terms of x.

Department 8 - 5 years, 4 months ago

@Department 8 – 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

Hamza A - 5 years, 4 months ago

I got 800\831

Gourav Khullar - 5 years, 4 months ago

Can you explain me how (the steps)

Department 8 - 5 years, 4 months ago

It's ans is 1

Gourav Khullar - 5 years, 4 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 :)

Hamza A - 5 years, 4 months ago

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

Department 8 - 5 years, 4 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 $1.3533\sqrt{x}$

Hamza A - 5 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$