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**NakulG****Member**- Registered: 2014-09-02
- Posts: 186

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

I am getting that too.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**NakulG****Member**- Registered: 2014-09-02
- Posts: 186

Hi BobbyM, so any thoughts how come the answer to this is said to be 3. Some videos on the web show the working but it is actually not solved, it is more like back calculation.

Also in this what is meant by -1, any thoughts.

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

I do not find any meaning of f(x) in 1st line since there is no x on R.H.S. In 2nd line it can be f(n) and 3rd line f(n+1).

Next if you call f(n) as y f(n+1) can not be replaced by y+1 because

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,354

hi NakulG

In your final line you have y = 3 or -1. Clearly the negative cannot be a solution to the original.

Incorrect answers can arise when you use squaring as a way to solve an equation. Consider this simple example:

x = 3 => x^2 = 9 => x^2 - 9 = 0 => (x-3)(x+3) = 0 => x = 3 or x = -3

So it is important to consider if an apparent answer actually fits the problem set. -1 doesn't. There is no more significance to that than x = -3 in my example.

Here's another: A rectangle is 2 units longer than it is wide. Its area is 15. What are its measurements?

Let the width be x. Then the length is x + 2 and x(x + 2) = 15 => x^2 + 2x - 15 = 0 => (x + 5)(x - 3) = 0 => x = 3 or -5

So the measurements are 3 and 5, or -5 and -3. Clearly this second 'answer' cannot be right as a rectangle cannot have a negative measurement.

This last example shows again how spurious answers can crop up.

Solve

Squaring

squaring again

I'll leave you to work out which is a solution and why the other appears.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

the expression is convergent as I found on excel sheet the sum of 100 terms taking the further portion =1 comes out tobe

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**NakulG****Member**- Registered: 2014-09-02
- Posts: 186

Thanks Bob, I will look into it.

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

I think value is 3 and not sqrt(3). i seem to have taken extra square root.

please refer to http://mathforum.org/library/drmath/view/52674.html

Date: 02/25/2002 at 21:01:47

From: Doctor Wilkinson

Subject: Re: Nested Radical

Nice problem, Mac! Here's the solution given by Ramanujan. You'll need

to fuss a bit about convergence.

Consider the identity

Take square roots to get

Now inside the brackets you have something + n, so you can substitute

in the same equation with x+n replacing x to get

and repeat the process to get

If you now set n = 1, x = 2 you get

*Last edited by thickhead (2016-05-07 04:27:36)*

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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