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NakulG

Member

Registered: 2014-09-02

Posts: 186

Is this solved corretly and if so what does -1 mean in this context

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this solved corretly and if so what does -1 mean in this context

Hi;

I am getting that too.

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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.

NakulG

Member

Registered: 2014-09-02

Posts: 186

Re: Is this solved corretly and if so what does -1 mean in this context

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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Is this solved corretly and if so what does -1 mean in this context

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

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{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.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,631

Re: Is this solved corretly and if so what does -1 mean in this context

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

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Is this solved corretly and if so what does -1 mean in this context

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

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{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.}

NakulG

Member

Registered: 2014-09-02

Posts: 186

Re: Is this solved corretly and if so what does -1 mean in this context

Thanks Bob, I will look into it.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Is this solved corretly and if so what does -1 mean in this context

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)

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{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.}