Math Is Fun Forum
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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
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
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
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
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
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: 10,623
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 
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#15 2014-11-16 03:42:16
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,623
Re: Find the value
See above.
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
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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: 10,623
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
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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: 10,623
Re: Find the value
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
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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
Re: Find the value
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
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.
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#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
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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