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#1 2014-03-04 04:36:19
- niharika_kumar
- Member
- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062
arithmetic progression.
If the sum of m terms of an AP is the same as the sum of its n terms, show that the sum of its (m+n) terms is zero.
friendship is tan 90°.
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#2 2014-03-04 05:28:52
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: arithmetic progression.
Hi;
This is what I got from researching it.
Got those 2 just from plugging in. Let's say they are equal and try to fight our way to a contradiction or maybe they are equal... Then
Clean up the LHS.
Times by -2.
Divide by m-n, do you see why we can do this?
If we just plug m+n into the formula for an arithmetic sum we get:
We know from A) that 2 a+d (m+n-1)=0 so
we are 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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#3 2014-03-04 15:08:18
- niharika_kumar
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- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062
Re: arithmetic progression.
m and n are equal.
thanks bobbym 
friendship is tan 90°.
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#4 2014-03-04 16:11:39
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: arithmetic progression.
m and n aren't equal. The fact that they are not allows us to divide by (m-n)...
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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
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#5 2014-03-04 16:16:04
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: arithmetic progression.
If m and n were equal could not divide by m-n because that would be 0. m ≠ n is a requirement.
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 2014-03-04 21:54:27
- niharika_kumar
- Member
- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062
Re: arithmetic progression.
oh sorry i had got something wrong in my mind at that time.
i had another question opened in front of me and by mistake I referred it here.
thanks for correcting it.
friendship is tan 90°.
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#7 2014-03-04 22:07:06
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: arithmetic progression.
Did you follow his idea? Or do you need more explanation.
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 2014-03-05 16:36:02
- niharika_kumar
- Member
- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062
Re: arithmetic progression.
yes i followed it.
if it would have been equal, the entire equation would have been not defined.
friendship is tan 90°.
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#9 2014-03-05 16:40:14
Re: arithmetic progression.
If m and n were equal could not divide by m-n because that would be 0. m ≠ n is a requirement.
Also, if m=n, then we can prove by a counterexample that the statement is false
'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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#10 2014-03-05 16:43:12
- niharika_kumar
- Member
- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062
Re: arithmetic progression.
yes.
friendship is tan 90°.
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