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#1 2013-11-24 06:14:18

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Mathematical proofs?

Hey guys.I just came out with a new problem i discovered.
Let it be n>=2 a natural number and n rational numbers with the property that,however we pick one of them,the sum of the other n-1 is 0.Show that all the numbers are equal to 0.
xD have fun

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#2 2013-11-24 06:27:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,354

Re: Mathematical proofs?

Let the numbers be

and
for
.

Then we have that

for
. We see that all of the numbers are the same. It is now obvious that they must all be zero.

Last edited by anonimnystefy (2013-11-24 06:28:02)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2013-11-25 02:08:10

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: Mathematical proofs?

Interesting proof,i thought of a different one.

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#4 2013-11-25 03:04:28

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 611
Website

Re: Mathematical proofs?

Let
.

For any

we have

Adding

to both sides gives
. As this is true for all
we have

Since we are given

we must have
i.e.
.


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#5 2013-11-25 05:47:23

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: Mathematical proofs?

How do you write mathematical here?
I mean with all the symbols and etc.

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#6 2013-11-25 06:40:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,354

Re: Mathematical proofs?

Use (math)(/math), except that you put [ and ] instead of ( and ). This enables you to use LaTeX on the forum.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2013-11-25 11:33:17

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,304

Re: Mathematical proofs?


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

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