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#1 2014-11-15 15:40:11

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

Find the value

Find the value of


friendship is tan 90°.

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#2 2014-11-15 15:42:26

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Find the value

KVPY question!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#3 2014-11-15 15:45:51

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

Re: Find the value

Hi;

The answer is readily obtained but how do you want it done?


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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#4 2014-11-15 15:48:06

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

Re: Find the value

anyhow, manually.

Did you appear in KVPY @agnishom.


friendship is tan 90°.

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#5 2014-11-15 15:55:04

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

Re: Find the value

Hi;

Where is the problem from?


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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#6 2014-11-15 16:05:12

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Find the value

I did.

The problem is from KVPY 2014.

I did it experimentally.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#7 2014-11-15 16:13:00

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

Re: Find the value

You are not going to find a simple closed form, I do not think it exists.


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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#8 2014-11-15 16:16:26

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Find the value

@niharika_kumar: May I have the options please?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#9 2014-11-15 16:20:45

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

Re: Find the value

That would help.


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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#10 2014-11-15 16:29:30

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Find the value


These are the first few terms that I can get by replacing 1947 with 1,2,3,4,5,6,7,8,9,10 respectively.

Last edited by Agnishom (2014-11-15 16:30:03)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#11 2014-11-15 16:35:53

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

Re: Find the value

Which 1947?


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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#12 2014-11-15 16:41:33

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Find the value

Both


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#13 2014-11-15 18:37:52

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

Re: Find the value

And what did you get for an answer?


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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#14 2014-11-16 02:32:24

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Find the value

hi Niharika,

This is my final and, I hope correct, version.

Consider the j-th term:

As this is a bit complicated I'm going to simplify by replacing 2^973 by K, and 2^j by L, so the expression becomes

Now there are an even number of terms in the sum, so find the one that is j from the end:

Add these two terms:

Thus you can pair up a term from the first half of the sum with another from the second half, and get the same j independent result every time.

There are 974 pairs so the sum is


Bob

Last edited by Bob (2014-11-16 03:43:37)


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 smile

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#15 2014-11-16 03:42:16

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Find the value

See above.  smile

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

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#16 2014-11-16 04:11:15

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

Re: Find the value

That is a nice solution Bob!


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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#17 2014-11-16 04:37:01

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Find the value

hi bobbym,

Thank you.  I had the ideas in my head hours ago but I kept slipping up with the algebra.  Making the K and L substitutions made a big difference as I was able to get rid of all those horrible powers.  One of my early errors actually allowed the cancelling, leading me into thinking I was on track.  Then I spotted a slip and the more I corrected the further I got from the nice answer.  My table top is now covered with sheets of paper with, mostly, wrong versions.  More for the paper re-cycling.

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

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#18 2014-11-16 04:45:24

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

Re: Find the value

Hi;

Could be a slogan: Save a tree, just say no to math.


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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#19 2014-11-16 04:52:37

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Find the value

smile

Someone will have to invent writing in the air, sort of like plane contrails.  Now that would be really useful.

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

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#20 2014-11-16 04:54:59

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

Re: Find the value

They used to write in the sand. Lots of space and erasable 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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#21 2014-11-16 12:06:11

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Find the value

bobbym wrote:

Hi;

Could be a slogan: Save a tree, just say no to math.

Math should be done on computers.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#22 2014-11-16 12:28:50

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

Re: Find the value

Yes, I agree. See Doron Zeilberger's lecture. Check computer math.


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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#23 2014-11-16 12:50:20

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Find the value

That is what computers were invented for!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#24 2014-11-16 12:55:50

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

Re: Find the value

That is not what computers were invented for.


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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#25 2014-11-16 19:43:41

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Find the value

What were computers invented for, then?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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