Waste less time on Facebook — follow Brilliant.
×

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
2 years, 2 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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

Sort by:

Top Newest

K

Gourav Khullar - 1 year, 10 months ago

Log in to reply

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, 10 months ago

Log in to reply

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

Lakshya Sinha - 1 year, 10 months ago

Log in to reply

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 - 1 year, 10 months ago

Log in to reply

It's ans is 1

Gourav Khullar - 1 year, 10 months ago

Log in to reply

I got 800\831

Gourav Khullar - 1 year, 10 months ago

Log in to reply

Can you explain me how (the steps)

Lakshya Sinha - 1 year, 10 months ago

Log in to reply

@Aditya Kumar

Lakshya Sinha - 1 year, 10 months ago

Log in to reply

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 - 1 year, 10 months ago

Log in to reply

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

Lakshya Sinha - 1 year, 10 months ago

Log in to reply

@Lakshya Sinha Do you have any reason to believe that the closed form exists in terms of elementary functions?

Ishan Singh - 1 year, 10 months ago

Log in to reply

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

Lakshya Sinha - 1 year, 10 months ago

Log in to reply

@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 - 1 year, 10 months ago

Log in to reply

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

Lakshya Sinha - 2 years ago

Log in to reply

solution?

Dev Sharma - 2 years, 1 month ago

Log in to reply

No solution yet! Big bang is a test of FIITJEE

Lakshya Sinha - 2 years, 1 month ago

Log in to reply

@Otto Bretscher

Lakshya Sinha - 2 years, 2 months ago

Log in to reply

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

Lakshya Sinha - 2 years, 2 months ago

Log in to reply

Please limit your tags to at most 5 people.

Nihar Mahajan - 2 years, 2 months ago

Log in to reply

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

Kaustubh Miglani - 2 years, 2 months ago

Log in to reply

whats big bang here??

Dev Sharma - 2 years, 1 month ago

Log in to reply

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

Lakshya Sinha - 2 years, 2 months ago

Log in to reply

@Lakshya Sinha no prob buddy i am gonna explode avec tension any idea if i am gonna come 1st or not

Kaustubh Miglani - 2 years, 2 months ago

Log in to reply

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

Lakshya Sinha - 2 years, 2 months ago

Log in to reply

please reply fast

Kaustubh Miglani - 2 years, 2 months ago

Log in to reply

Comment deleted Mar 31, 2016

Log in to reply

The graph by hummus a

Lakshya Sinha - 1 year, 10 months ago

Log in to reply

Hmm…

Swapnil Das - 1 year, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...